Eur. Phys. J. Special Topics 228, 261-623 (2019) © The Author(s) 2019 https://doi.org/10.1140/epjst/e2019-900045-4 THE EUROPEAN PHYSICAL JOURNAL Special Topics Regular Article FCC -ee: The Lepton Collider Future Circular Collider Conceptual Design Report Volume 2 A. Abada32, M. Abbrescia117,257, S.S. AbdusSalam218, I. Abdyukhanov16, J. Abelleira Fernandez142, A. Abramov204, M. Aburaia284, A.O. Acar238, P.R. Adzic287, P. Agrawal79, J.A. Aguilar-Saavedra46, J.J. Aguilera-Verdugo106, M. Aiba191, I. Aichinger64, G. Aielli134,272, A. Akay238, A. Akhundov45, H. Aksakal145, J.L. Albacete46, S. Albergo120,260, A. Alekou311, M. Aleksa64, R. Aleksan39, R.M. Alemany Fernandez64, Y. Alexahin70, R.G. Alia64, S. Alioli126, N. Alipour Tehrani64, B.C. Allanach298, P.P. Allport290, M. Altinli112,62, W. Altmannshofer297, G. Ambrosio70, D. Amorim64, O. Amstutz161, L. Anderlini123,262, A. Andreazza127,266, M. Andreini64, A. Andriatis167, C. Andris165, A. Andronic344, M. Angelucci115, F. 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Osland288, T. Otto64, K.Y. Oyulmaz2, A. Ozansoy9, V. Ozcan19, K. Ozdemir195, C.E. Pagliarone114,52,112, H.F. Pais da Silva64, E. Palmieri116, L. Palumbo133,271, A. Pampaloni124,263, R.-Q. Pan348, M. Panareo125,265, O. Panella131,270, G. Panico262, G. Panizzo137,275, A.A. Pankov76, V. Pantsyrny16, C.G. Papadopoulos176, A. Papaefstathiou175, Y. Papaphilippou64, M.A. Parker298, V. Parma64, M. Pasquali64, S.K. Patra87, R. Patterson44, H. Paukkunen306, F. Pauss59, S. Peggs20, J.-P. Penttinen201, G. Peán64, E.E. Perepelkin143, E. Perez64, J.C. Perez64, G. Perez342, F. Perez6, E. Perez Codina64, J. Perez Morales34, M. Perfilov221, H. Pernegger64, M. Peruzzi64, C. Pes39, K. Peters49, S. Petracca113, F. Petriello187, L. Pezzotti130,269, S. Pfeiffer232, F. Piccinini130,269, T. Pieloni56, M. Pierini64, H. Pikhartova204, G. Pikurs203, E. Pilicer244, P. Piminov23, C. Pira116, R. Pittau46, W. Płaczek166, M. Plagge64,189, T. Plehn277, M.-A. Pleier20, M. Płoskoń160, M. Podeur326, H. Podlech91, FCC-ee: The Lepton Collider 265 T. Podzorny64, L. Poggioli32, A. Poiron57, G. Polesello130,269, M. Poli Lener115, A. Polini118,258, J. Polinski346, S.M. Polozov180, L. Ponce64, M. Pont6, L. Pontecorvo133,271, T. Portaluri59, K. Potamianos49, C. Prasse71, M. Prausa7, A. Preinerstorfer12, E. Premat26, T. Price290, M. Primavera125, F. Prino136,274, M. Prioli127, J. Proudfoot11, A. Provino43, T. Pugnat39, N. Pukhaeva143, S. Puławski324, D. Pulikowski64,345, G. Punzi132,215, M. Putti263, A. Pyarelal285, H. Quack230, M. Quispe6, A. Racioppi178, H. Rafique311, V. Raginel77, M. Raidal178, N.S. Ramírez-Uribe103, M.J Ramsey-Musolf313, R. Rata64, P. Ratoff37, F. Ravotti64, P. Rebello Teles33, M. Reboud152, S. Redaelli64, E. Renner232, A.E. Rentería-Olivo104, M. Rescigno133,271, J. Reuter49, A. Ribon64, A.M. Ricci124,263, W. Riegler64, S. Riemann50, B. Riemann229, T. Riemann324, J.M. Rifflet39, R.A. Rimmer237, R. Rinaldesi64, L. Rinolfi64, O. Rios Rubiras64, T. Risselada64, A. Rivetti136,274, L. Rivkin191, T. Rizzo225, T. Robens205, F. Robert26, A.J. Robson303, E. Rochepault39, C. Roda132,215, G. Rodrigo106, M. Rodríguez-Cahuantzi15, C. Rogan307, M. Roig3, S. Rojas- Torres245, J. Rojo175, G. Rolandi132,215, G. Rolando64,191, P. Roloff64, A. Romanenko70, A. Romanov88, F. Roncarolo64, A. Rosado Sanchez15, G. Rosaz64, L. Rossi64,266, A. Rossi131,270, R. Rossmanith49,146, B. Rousset40, C. Royon307, X. Ruan328, I. Ruehl64, V. Ruhlmann-Kleider39, R. Ruiz54, L. Rumyantsev55,222, R. Ruprecht146, A.I. Ryazanov179, A. Saba43, R. Sadykov55, D. Saez de Jauregui146, M. Sahin337, B. Sailer22, M. Saito236, F. Sala49, G.P. Salam190, J. Salfeld-Nebgen197, C.A. Salgado108, S. Salini266, J.M. Sallese56, T. Salmi201, A. Salzburger64, O.A. Sampayo107, S. Sanfilippo191, J. Santiago46, E. Santopinto124, R. Santoro127,264, A. Sanz Ull60, X. Sarasola191, I.H. Sarpün5, M. Sauvain159, S. Savelyeva230, R. Sawada236, G.F.R. Sborlini45,109, A. Schaffer32, M. Schaumann64, M. Schenk64, C. Scheuerlein64, I. Schienbein155, K. Schlenga22, H. Schmickler64, R. Schmidt64,228, D. Schoerling64, T. Schoerner-Sadenius49, A. Schoning206, M. Schott198, D. Schulte64, P. Schwaller141, C. Schwanenberger49, P. Schwemling39, N. Schwerg64, L. Scibile64, A. Sciuto120,260, E. Scomparin136,274, C. Sebastiani133,271, B. Seeber303,213, M. Segreti39, P. Selva161, M. Selvaggi64, C. Senatore303, A. Senol2, L. Serin32, M. Serluca152, N. Serra333, A. Seryi142, L. Sestini129,267, A. Sfyrla303, M. Shaposhnikov56, E. Shaposhnikova64, B.Y. Sharkov143, D. Shatilov23, J. Shelton304, V. Shiltsev70, I.P. Shipsey190, G.D. Shirkov143, A. Shivaji130,269, D. Shwartz23, T. Sian311,301,211, S. Sidorov191, L. Silvestrini133,271, N. Simand27, F. Simon169, B.K. Singh13, A. Siódmok99, Y. Sirois32, E. Sirtori28, R. Sirvinskaite211,162, B. Sitar38, T. Sjüstrand309, P. Skands171, E. Skordis64,308, K. Skovpen340, M. Skrzypek99, E. Slade190, P. Slavich156, R. Slovak68, V. Smaluk20, V. Smirnov221, W. Snoeys64, L. Soffi44, P. Sollander64, O. Solovyanov93, H.K. Soltveit277, H. Song285, P. Sopicki99, M. Sorbi127,266, L. Spallino115, M. Spannowsky54, B. Spataro133,271, P. Sphicas64, H. Spiesberger198, P. Spiller77, M. Spira191, T. Srivastava87, J. Stachel277, A. Stakia64, J.L. Stanyard64, E. Starchenko179, A.Y. Starikov143, A.M. Stasto235, M. Statera127,266, R. Steerenberg64, J. Steggemann64, A. Stenvall201, F. Stivanello116, D. Stockinger230, L.S. Stoel64, M. Stüger- Pollach232, B. Strauss47,96, M. Stuart64, G. Stupakov225, S. Su285, A. Sublet64, K. Sugita77, L. Sulak18, M.K. Sullivan225, S. Sultansoy238, T. Sumida150, K. Suzuki81, G. Sylva43, M.J. Syphers186, A. Sznajder251, M. Taborelli64, N.A. Tahir77, M. Takeuchi236, E. Tal Hod233, C. Tambasco56, J. Tanaka236, K. Tang167, I. Tapan244, S. Taroni317, G.F. Tartarelli127,266, G. Tassielli125,265, L. Tavian64, T.M. Taylor64, G.N. Taylor314, A.M. Teixeira32,30, G. Tejeda- Muñoz15, V.I. Telnov23,188, R. Tenchini132,215, H.H.J. ten Kate64, K. Terashi236, A. Tesi123,262, M. Testa115, C. Tetrel27, D. Teytelman51, J. Thaler167, A. Thamm64, S. Thomas207, M.T. Tiirakari64, V. Tikhomirov95, D. Tikhonov80, 266 The European Physical Journal Special Topics H. Timko64, V. Tisserand32,30, L.M. Tkachenko143, J. Tkaczuk282,40, J.P. Tock64, B. Todd64, E. Todesco64, R. Tomás Garcia64, D. Tommasini64, G. Tonelli132,215, F. Toral34, T. Torims203, R. Torre64, Z. Townsend64, R. Trant64, D. Treille64, L. Trentadue126,268, A. Tricoli20, A. Tricomi120,260, W. Trischuk329, I.S. Tropin70, B. Tuchming39, A.A. Tudora64, B. Turbiarz99, I. Turk Cakir75, M. Turri266, T. Tydecks64, J. Usovitsch240, J. Uythoven64, R. Vaglio43, A. Valassi64, F. Valchkova64, M.A. Valdivia Garcia246, P. Valente127,266, R.U. Valente271, A.-M. Valente-Feliciano237, G. Valentino310, L. Vale Silva327, J.M. Valet27, R. Valizadeh211, J.W.F. Valle106, S. Vallecorsa74, G. Vallone160, M. van Leeuwen175, U.H. van Rienen320, L. van Riesen-Haupt142, M. Varasteh64, L. Vecchi56, P. Vedrine39, G. Velev70, R. Veness64, A. Ventura125,256, W. Venturini Delsolaro64, M. Verducci135,273, C.B. Verhaaren293, C. Vernieri70, A.P. Verweij64, O. Verwilligen117,257, O. Viazlo64, A. Vicini127,266, G. Viehhauser190, N. Vignaroli129,267, M. Vignolo43, A. Vitrano39, I. Vivarelli327, S. Vlachos182, M. Vogel279, D.M. Vogt326, V. Volkl92, P. Volkov221, G. Volpini127,266, J. von Ahnen49, G. Vorotnikov221, G.G. Voutsinas64, V. Vysotsky8, U. Wagner64, R. Wallny59, L.-T. Wang299, R. Wang11, K. Wang347, B.F.L. Ward14,343, T.P. Watson138, N.K. Watson290, Z. Was99, C. Weiland196, S. Weinzierl198, C.P. Welsch308, J. Wenninger64, M. Widorski64, U.A. Wiedemann64, H.-U. Wienands11, G. Wilkinson190, P.H. Williams211, A. Winter290, A. Wohlfahrt71, T. Wojtoá99, D. Wollmann64, J. Womersley66, D. Woog64, X. Wu303, A. Wulzer129,267, M.K. Yanehsari209, G. Yang148, H.J. Yang219,243, W.-M. Yao160, E. Yazgan97, V. Yermolchik95, A. Yilmaz112, A. Yilmaz75, H.-D. Yoo216, S.A. Yost234, T. You298, C. Young225, T.-T. Yu318, F. Yu141, A. Zaborowska64, S.G. Zadeh320, M. Zahnd57, M. Zanetti129,267, L. Zanotto116, L. Zawiejski99, P. Zeiler63, M. Zerlauth64, S.M. Zernov72, G. Zevi Dell Porta295, Z. Zhang32, Y. Zhang341, C. Zhang192, H. Zhang97, Z. Zhao322, Y.-M. Zhong18, J. Zhou130,269, D. Zhou81, P. Zhuang242, G. Zick3, F. Zimmermann64, J. Zinn- Justin39, L. Zivkovic287, A.V. Zlobin70, M. Zobov115, J. Zupan300, J. Zurita146, and the FCC Collaboration352 1 A.I. Alikhanyan National Science Laboratory (YerPhi), Yerevan, Armenia 2 Abant Izzet Baysal University (AIBU), Bolu, Turkey 3 Air Liquide Advanced Technologies (ALAT), Sassenage, France 4 Aix-Marseille Université (AMU), Marseille, France 5 Akdeniz University (UAKDENIZ), Antalya, Turkey 6 ALBA Synchrotron - Consorcio para la Construcción, Equipamiento y Explotación del Laboratorio de Luz Sincrotrón, Cerdanyola del Valles (CELLS-ALBA), Cerdanyola del Valles, Spain 7 Albert-Ludwigs-Universitat Freiburg (UFreiburg), Freiburg, Germany 8 All-Russian Scientific Research and Development Cable Institute (VNIIKP), Moscow, Russia 9 Ankara University (Ankara U), Tandogan, Ankara, Turkey 10 Applied Superconductivity Center (ASC), Tallahassee, FL, USA 11 Argonne National Laboratory (ANL), Argonne, IL, USA 12 Austrian Institute of Technology (AIT), Vienna, Austria 13 Banaras Hindu University (BHU), Varanasi, India 14 Baylor University (Baylor), Waco, TX, USA 15 Benemerita Universidad Autónoma de Puebla (BUAP), Puebla, Mexico 16 Bochvar Institute of Inorganic Materials (VNIINM), Moscow, Russia 17 Bogoliubov Laboratory of Theoretical Physics (BLTP JINR), Dubna, Russia 18 Boston University (BU), Boston, MA, USA 19 Bogazici University (BOUN), Istanbul, Turkey FCC-ee: The Lepton Collider 267 20 Brookhaven National Laboratory (BNL), Upton, NY, USA 21 Brown University (Brown), Providence, RI, USA 22 BRUKER EST (Bruker), Hanau, Germany 23 Budker Institute of Nuclear Physics (BINP), Novosibirsk, Russia 24 Center for High Energy Physics (CHEP), Daegu, Republic of Korea 25 Centre de Physique des Particules de Marseille (CPPM), Marseille, France 26 Centre d’Etudes des Tunnels (CETU), Bron, France 27 Centre d’etudes et d’expertise sur les risques, l’environnement, la mobilité et l’amenagement (CEREMA), Lyon, France 28 Centre for Industrial Studies (CSIL), Milan, Italy 29 Centre National de la Recherche Scientifique (CNRS), Aubiere, France 30 Centre National de la Recherche Scientifique (CNRS/IN2P3), Clermont-Ferrand, France 31 Centre National de la Recherche Scientifique (CNRS), Marseille, France 32 Centre National de la Recherche Scientifique (CNRS), Paris, France 33 Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil 34 Centro de Investigaciones Energeticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain 35 Centro de Investigacion y de Estudios Avanzados (CINVESTAV), Merdia, Mexico 36 Cockcroft Institute (CI Daresbury), Daresbury, UK 37 Cockcroft Institute (CI Lancaster), Lancaster, UK 38 Comenius University (CU), Bratislava, Slovakia 39 Commissariat à l’energie atomique et aux energies alternatives - Institut de Recherche sur les lois Fondamentales de l’Univers Saclay (CEA/DSM/Irfu Saclay), Gif-sur-Yvette, France 40 Commissariat à l’energie atomique et aux energies alternatives - Institut Nanosciences et Cryogenie (CEA), Grenoble, France 41 Consiglio Nazionale delle Ricerche (CNR), Milan, Italy 42 Consiglio Nazionale delle Ricerche - Superconducting and other Innovative materials and devices institute (CNR-SPIN), Genoa, Italy 43 Consiglio Nazionale delle Ricerche - Superconducting and other Innovative materials and devices institute (CNR-SPIN), Naples, Italy 44 Cornell University (Cornell), Ithaca, NY, USA 45 Departamento de Física Teorica, Universidad de Valencia (UV), Valencia, Spain 46 Departamento de Física Teórica y del Cosmos and CAFPE, Universidad de Granada (UGR), Granada, Spain 47 Department of Energy (DoE), Washington, DC, USA 48 Department of Physics, University of Tehran (UT), Tehran, Iran 49 Deutsches Elektronen Synchrotron (DESY), Hamburg, Germany 50 Deutsches Elektronen Synchrotron (DESY ZEU), Zeuthen, Germany 51 Dimtel, Inc. (Dimtel), San Jose, CA, USA 52 Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale (DICEM), Cassino, Italy 53 Duke University (DU), Durham, NC, USA 54 Durham University, Institute for Particle Physics Phenomenology (IPPP), Durham, UK 55 Dzhelepov Laboratory of Nuclear Problems (DLNP JINR), Dubna, Russia 56 Ecole polytechnique federale de Lausanne (EPFL), Lausanne, Switzerland 57 Ecotec Environnement SA (Ecotec), Geneva, Switzerland 58 Ege University (EgeU), Izmir, Turkey 59 Eidgenössische Technische Hochschule Zürich (ETHZ), Zürich, Switzerland 60 Eindhoven University of Technology (TU/e), Eindhoven, The Netherlands 61 Elle Marmi SARL (EM), Carrara, Italy 62 Eskisehir Technical University (ESTU), Istanbul, Turkey 63 Esslingen University of Applied Sciences (HS Esslingen), Goppingen, Germany 64 European Organization for Nuclear Research (CERN), Geneva, Switzerland 65 European Scientific Institute (ESI), Archamps, France 268 The European Physical Journal Special Topics 66 European Spallation Source (ESS), Lund, Sweden 67 Fachhochschule Südwestfalen (FH-SWF), Gelsenkirchen, Germany 68 Faculty of Mathematics and Physics, Charles University Prague (CU), Prague, Czech Republic 69 Fayoum University (FU), El-Fayoum, Egypt 70 Fermi National Accelerator Laboratory (FNAL), Batavia, IL, USA 71 Fraunhofer-Institut fur Materialfluss und Logistik (FIML), Dortmund, Germany 72 Fuel Company of Rosatom TVEL (TVEL), Moscow, Russia 73 Fujikura Ltd. (Fujikura), Sakura City, Japan 74 Gangneung-Wonju National University (GWNU), Gangneung-Wonju, Republic of Korea 75 Giresun University (Giresun), Giresun, Turkey 76 Gomel State Technical University (GSTU), Gomel, Belarus 77 GSI Helmholtz Zentrum fur Schwerionenforschung (GSI), Darmstadt, Germany 78 Gumushane University (Gumushane), Gumushane, Turkey 79 Harvard University (Harvard), Cambridge, MA, USA 80 Helmholtz-Zentrum Berlin (HZB), Berlin, Germany 81 High Energy Accelerator Research Organization (KEK), Tsukuba, Japan 82 Isik University (Isikun), Istanbul, Turkey 83 I-Cube Research (I-Cube), Toulouse, France 84 II. Institut fur Theoretische Physik, Universität Hamburg (UNITH), Hamburg, Germany 85 ILF Consulting Engineers (ILF), Zürich, Switzerland 86 Indian Institute of Technology Guwahati (IITG), Guwahati, India 87 Indian Institute of Technology Kanpur (IITK), Kanpur, Uttar Pradesh, India 88 Institut de Ciencia de Materials de Barcelona (ICMAB-CSIC), Barcelona, Spain 89 Institut de Physique Nucléaire d’Orsay (CNRS/IN2P3/IPNO), Orsay, France 90 Institute for Advanced Study (IAS), Princeton, NJ, USA 91 Institute for Applied Physics, Goethe University (IAP), Frankfurt, Germany 92 Institute for Astro and Particle Physics, University of Innsbruck (UIBK), Innsbruck, Austria 93 Institute for High Energy Physics of NRC “Kurchatov Institute” (IHEP), Protvino, Russia 94 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University (IMAPP), Nijmegen, The Netherlands 95 Institute for Nuclear Problems of Belarusian State University (INP BSU), Minsk, Belarus 96 Institute of Electrical and Electronic Engineers (IEEE), Piscataway, NJ, USA 97 Institute of High Energy Physics, Chinese Academy of Science, Beijing (IHEP CAS), Beijing, P.R. China 98 Institute of Machine Components, University of Stuttgart (IMA), Stuttgart, Germany 99 Institute of Nuclear Physics Polish Academy of Sciences (IFJ PAN), Krakow, Poland 100 Institute of Physics, Academia Sinica (AS), Taipei, Taiwan 101 Institut Jozef Stefan (IJS), Ljubljana, Slovenia 102 Instituto de Astrofísica de Canarias (IAC), La Laguna, Spain 103 Instituto de Física Corpuscular (CSIC-UV), Paterna, Spain 104 Instituto de Física Corpuscular (CSIC-UV), Valencia, Spain 105 Instituto de Física Teórica, Universidad Autonoma de Madrid (IFT-UAM), Madrid, Spain 106 Instituto de Física, Universitat de Valencia (CSIC), Valencia, Spain 107 Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Mar del Plata, Argentina 108 Instituto Galego de Física de Altas Enxerxías, Universidade de Santiago de Compostela (IGFAE), Santiago de Compostela, Spain 109 International Center for Advanced Studies, Universidad Nacional de San Martin (ICAS- UNSAM), San Martin, Argentina 110 Iowa State University (ISU), Ames, IA, USA FCC-ee: The Lepton Collider 269 111 Istanbul Aydin University (IAU), Istanbul, Turkey 112 Istanbul University (iU), Istanbul, Turkey 113 Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno - Sezione di Napoli (INFN SA), Salerno, Italy 114 Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso (INFN LNGS), Assergi (L’Aquila), Italy 115 Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati (INFN LNF), Frascati, Italy 116 Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro (INFN LNLN), Legnaro, Italy 117 Istituto Nazionale di Fisica Nucleare Sezione di Bari (INFN BA), Bari, Italy 118 Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (INFN BO), Bologna, Italy 119 Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari (INFN CA), Cagliari, Italy 120 Istituto Nazionale di Fisica Nucleare, Sezione di Catania (INFN CT), Catania, Italy 121 Istituto Nazionale di Fisica Nucleare, Sezione di Cosenza (INFN CS), Cosenza, Italy 122 Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara (INFN FE), Ferrara, Italy 123 Istituto Nazionale di Fisica Nucleare, Sezione di Firenze (INFN FI), Florence, Italy 124 Istituto Nazionale di Fisica Nucleare, Sezione di Genova (INFN GE), Genoa, Italy 125 Istituto Nazionale di Fisica Nucleare, Sezione di Lecce (INFN LE), Lecce, Italy 126 Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca (INFN MIB), Milan, Italy 127 Istituto Nazionale di Fisica Nucleare, Sezione di Milano (INFN MI), Milan, Italy 128 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN NA), Naples, Italy 129 Istituto Nazionale di Fisica Nucleare, Sezione di Padova (INFN PD), Padua, Italy 130 Istituto Nazionale di Fisica Nucleare, Sezione di Pavia (INFN PV), Pavia, Italy 131 Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (INFN PG), Perugia, Italy 132 Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Universita di Pisa (INFN PI), Pisa, Italy 133 Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1 (INFN Roma 1), Rome, Italy 134 Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata (INFN Roma 2), Rome, Italy 135 Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre (INFN Roma 3), Rome, Italy 136 Istituto Nazionale di Fisica Nucleare, Sezione di Torino (INFN TO), Turin, Italy 137 Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (INFN TS), Trieste, Italy 138 ITER (ITER), Cadarache, France 139 Ivane Javakhishvili T’bilisi State University (TSU), T’bilisi, Georgia 140 Izmir University of Economics (IUE), Izmir, Turkey 141 Johannes-Gutenberg-Universitat (JGU), Mainz, Germany 142 John Adams Institute for Accelerator Science, The Chancellor, Masters and Scholars of the University of Oxford (JAI), Oxford, UK 143 Joint Institute for Nuclear Research (JINR), Dubna, Russia 144 Julius-Maximilians-Universitat Würzburg (UWUERZBURG), Würzburg, Germany 145 Kahramanmaras Sutcu Imam University (KSU), Kahramanmaras, Turkey 146 Karlsruher Institut fuür Technologie (KIT), Karlsruhe, Germany 147 Katholieke Universiteit Leuven Research & Development (LRD), Louvain, Belgium 148 Key Laboratory of Theoretical Physics, Chinese Academy of Science (SKLTP ITP CAS), Beijing, P.R. China 149 King’s College London (KCL), London, UK 150 Kyoto University (Kyodai), Kyoto, Japan 151 Kyungpook National University (KNU), Sankyuk-dong, Republic of Korea 152 Laboratoire d’Annecy-Le-Vieux de Physique des Particules (CNRS/IN2P3/LAPP), Annecy, France 153 Laboratoire de l’Accelerateur Linéaire, Université de Paris Sud (CNRS/IN2P3/UPSUD/ LAL), Orsay, France 154 Laboratoire de Physique Nucleaire et de Hautes Energies (LPNHE), Paris, France 270 The European Physical Journal Special Topics 155 Laboratoire de Physique Subatomique et de Cosmologie Grenoble (LPSC), Grenoble, France 156 Laboratoire de Physique Théorique et Hautes Energies (CNRS/Sorbonne/LPTHE), Paris, France 157 Laboratoire Leprince-Ringuet, Ecole Polytechnique (LLR), Palaiseau, France 158 Laboratorio de Instrumentaçâo e Física Experimental de Partículas (LIP), Lisbon, Portugal 159 Latitude Durable (LD), Geneva, Switzerland 160 Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA, USA 161 Linde Kryotechnik AG (Linde), Pfungen, Switzerland 162 Loughborough University (LBoro), Loughborough, UK 163 Ludwig Maximilians University of Munich (LMU), Munich, Germany 164 Luvata Pori Oy (Luvata), Pori, Finland 165 MAN Energy Solutions Schweiz AG (MAN ES), Zurich, Switzerland 166 Marian Smoluchowski Institute of Physics, Jagiellonian University (UJ), Krakow, Poland 167 Massachusetts Institute of Technology (MIT), Cambridge, MA, USA 168 Max-Planck-Institut fur Kernphysik (MPIK), Heidelberg, Germany 169 Max-Planck-Institut fur Physik (MPP), Munich, Germany 170 Ministère de l’Europe et des Affaires etrangeres (MEAE), Paris, France 171 Monash University (Monash), Melbourne, Australia 172 MTA Wigner Research Centre for Physics (Wigner), Budapest, Hungary 173 Mustafa Kemal Universitesi (MKU), Hatay, Turkey 174 Nankai University (NKU), Tianjin, P.R. China 175 Nationaal instituut voor subatomaire fysica (NIKHEF), Amsterdam, The Netherlands 176 National Centre for Scientific Research Demokritos (NCSRD), Athens, Greece 177 National High Magnetic Field Laboratory, Florida State University (MagLab), Tallahassee, FL, USA 178 National Institute of Chemical Physics and Biophysics (NICPB), Tallin, Estonia 179 National Research Center Kurchatov Institute (NRCKI), Moscow, Russia 180 National Research Nuclear University MEPhI (MEPhI), Moscow, Russia 181 National Science Centre Kharkov Institute of Physics and Technology (KIPT), Kharkov, Ukraine 182 National Technical University of Athens (NTUA), Athens, Greece 183 Naturhistorisches Museum Wien (NHM), Vienna, Austria 184 Niels Bohr Institute, Copenhagen University (NBI), Copenhagen, Denmark 185 Nigde Omer Halisdemir University (OHU), Nigde, Turkey 186 Northern Illinois University (NIU), DeKalb, IL, USA 187 Northwestern University (NU), Evanston, IL, USA 188 Novosibirsk State University (NSU), Novosibirsk, Russia 189 Otto-von-Guericke-Universityät Magdeburg (OVGU), Magdeburg, Germany 190 Oxford University (UOXF), Oxford, UK 191 Paul Scherrer Institute (PSI), Villigen, Switzerland 192 Peking University (PU), Beijing, P.R. China 193 Perimeter Institute for Theoretical Physics (PI), Watterloo, Canada 194 Petersburg Nuclear Physics Institute, NRC “Kurchatov Institute” (PNPI), Gatchina, Russia 195 Piri Reis University (PRU), Istanbul, Turkey 196 Pittsburgh Particle physics, Astrophysics & Cosmology Center and Department of Physics & Astronomy, University of Pittsburgh (PITT PACC), Pittsburgh, PA, USA 197 Princeton University (PU), Princeton, NJ, USA 198 PRISMA Cluster of Excellence, Inst. fuär Physik, Johannes-Gutenberg-Universitäat (PRISMA), Mainz, Germany 199 Pusan National University (PNU), Busan, Republic of Korea 200 Queen’s University (Queens U), Kingston, Canada 201 RAMENTOR Oy (RAMENTOR), Tampere, Finland FCC-ee: The Lepton Collider 271 202 Rheinisch-Westfalische Technische Hochschule Aachen (RWTH), Aachen, Germany 203 Riga Technical University (RTU), Riga, Latvia 204 Royal Holloway University (RHUL), London, UK 205 Ruder Boskovic Institute (RBI), Zagreb, Croatia 206 Ruprecht Karls Universitat Heidelberg (RKU), Heidelberg, Germany 207 Rutgers, The State University of New Jersey (RU), Piscataway, NJ, USA 208 Sapienza Università di Roma (UNIROMA1), Rome, Italy 209 School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran 210 School of Physics and Astronomy, University of Glasgow (SUPA), Glasgow, UK 211 Science and Technology Facilities Council, Daresbury Laboratory (STFC DL), Warrington, UK 212 Science and Technology Facilities Council, Appleton Laboratory (STFC RAL), Rutherford, Didcot, UK 213 scMetrology SARL (scMetrology), Geneva, Switzerland 214 Scuola Int. Superiore di Studi Avanzati di Trieste (SISSA), Trieste, Italy 215 Scuola Normale Superiore (SNS), Pisa, Italy 216 Seoul National University (SNU), Seoul, Republic of Korea 217 Sevaplan und Wurm Schweiz AG (WURM), Winterthur, Switzerland 218 Shahid Beheshti University (SBUT), Tehran, Iran 219 Shanghai Jiao Tong University (SJTU), Shanghai, P.R. China 220 Shirokuma GmbH (Shirokuma), Wetzikon, Switzerland 221 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University (SINP MSU), Moscow, Russia 222 Southern Federal University (SFU), Rostov-on-Don, Russia 223 Southern Methodist University (SMU), Dallas, TX, USA 224 Sri Guru Tegh Bahadur Khalsa College, University of Delhi (SGTB Khalsa College), New Delhi, India 225 Stanford National Accelerator Center (SLAC), Menlo Park, CA, USA 226 Stanford University (SU), Stanford, cA, USA 227 Stony Brook University (SBU), Stony Brook, NY, USA 228 Technische Universitüat Darmstadt (TU Darmstadt), Darmstadt, Germany 229 Technische Universitaüt Dortmund (TU Dortmund), Dortmund, Germany 230 Technische Universitüat Dresden (TU Dresden), Dresden, Germany 231 Technische Universitüat Graz (TU Graz), Graz, Austria 232 Technische Universitüat Wien (TU Wien), Vienna, Austria 233 Tel Aviv University (TAU), Tel Aviv, Israel 234 The Citadel, The Military College of South Carolina (Citadel), Charleston, SC, USA 235 The Pennsylvania State University (PSU), University Park, PA, USA 236 The University of Tokyo (Todai), Tokyo, Japan 237 Thomas Jefferson National Accelerator Facility (JLab), Newport News, VA, USA 238 TOBB University of Economics and Technology (TOBB ETU), Ankara, Turkey 239 Tokyo Institute of Technology (Tokyo Tech), Tokyo, Japan 240 Trinity College Dublin (TCD), Dublin, Ireland 241 Tri-University Meson Facility (TRIUMF), Vancouver, Canada 242 Tsinghua University (THU), Beijing, P.R. China 243 Tsung-Dao Lee Institute (TDLI), Shanghai, P.R. China 244 Uludag University (ULU!)), Bursa, Turkey 245 Universidad Autonoma de Sinaloa (UAS), Culiacan, Mexico 246 Universidad de Guanajuato (UGTO), Guanajuato, Mexico 247 Universidad de La Laguna (ULL), La Laguna, Spain 248 Universidad de la Republica (Udelar), Montevideo, Uruguay 249 Universidad de los Andes (Uniandes), Bogota, Colombia 250 Universidade de Sao Paulo (USP), Sao Paulo, Brazil 251 Universidade do Estado do Rio de Janeiro (UERJ), Rio de Janeiro, Brazil 272 The European Physical Journal Special Topics 252 Universidade Federal de Pelotas (UFPel), Pelotas, Brazil 253 Universidade Federal de Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 254 Università degli Studi Roma Tre - Centro Ricerche Economiche e Sociali Manlio Rossi-Doria (EDIRC), Rome, Italy 255 Università della Calabria (UNICAL), Arcavacata, Italy 256 Universita del Salento (UNISALENTO), Lecce, Italy 257 Università di Bari (UNIBA), Bari, Italy 258 Universita di Bologna (UNIBO), Bologna, Italy 259 Università di Cagliari (UNICA), Cagliari, Italy 260 Universita di Catania (uNICt), Catania, Italy 261 Universita di Ferrara (UNIFE), Ferrara, Italy 262 Università di Firenze (UNIFI), Florence, Italy 263 Universita di Genova (UNIGE), Genoa, Italy 264 Universita di Insubria (UNINSUBRIA), Milan, Italy 265 Universita di Lecce(UNILE), Lecce, Italy 266 Università di Milano (UNIMI), Milan, Italy 267 Università di Padova (UNIPD), Padua, Italy 268 Università di Parma (UNIPR), Parma, Italy 269 Universita di Pavia (UNIPV), Pavia, Italy 270 Universita di Perugia (UNIPG), Perugia, Italy 271 Universita di Roma Sapienza (UNIROMA1), Rome, Italy 272 Universita di Roma Tor Vergata (UNIROMA2), Rome, Italy 273 Universita di Roma Tre (UNIROMA3), Rome, Italy 274 Universita di Torino (UNITO), Turin, Italy 275 Universita di Udine (UNIUD), Udine, Italy 276 Universität Hamburg (UHH), Hamburg, Germany 277 Universitat Heidelberg (HEI), Heidelberg, Germany 278 Universitat Politecnica de Catalunya (UPC), Barcelona, Spain 279 Universitat Siegen (U Siegen), Siegen, Germany 280 Universitaüt Tuübingen (TU), Tuübingen, Germany 281 Universite Clermont Auvergne (UCA), Aubiere, France 282 Universite Grenoble Alpes (UGA), Grenoble, France 283 University College London (UCL), London, UK 284 University of Applied Sciences Technikum Wien (UAS TW), Vienna, Austria 285 University of Arizona (UA), Tucson, AZ, USA 286 University of Basel(UNIBAS), Basel, Switzerland 287 University of Belgrade (UB), Belgrade, Serbia 288 University of Bergen (UiB), Bergen, Norway 289 University of Bern (UNIBE), Bern, Switzerland 290 University of Birmingham (UBIRM), Birmingham, UK 291 University of Bristol (UOB), Bristol, UK 292 University of California Berkeley (UCB), Berkeley, CA, USA 293 Davis (UCD), University of California, Davis, CA, USA 294 Irvine (UCI), University of California, Irvine, CA, USA 295 San Diego (UCSD), University of California, San Diego, CA, USA 296 University of California Santa Barbara (UCSB), Santa Barbara, CA, USA 297 University of California Santa Cruz (UCSC), Santa Cruz, CA, USA 298 University of Cambridge (CAM), Cambridge, UK 299 University of Chicago (UCHI), Chicago, IL, USA 300 University of Cincinnati (Uc), Cincinnati, OH, USA 301 University of Edinburgh (ED), Edinburgh, UK 302 University of Florida (UF), Gainesville, FL, USA 303 University of Geneva (UniGE), Geneva, Switzerland 304 University of Illinois at Urbana Champaign (UIUC), Urbana Champaign, IL, USA 305 University of Iowa (UIowa), Iowa City, IA, USA FCC-ee: The Lepton Collider 273 306 University of Jyvaskylä (JYU), Jyväskyla, Finland 307 University of Kansas (KU), Lawrence, KS, USA 308 University of Liverpool (ULIV), Liverpool, UK 309 University of Lund (ULU), Lund, Sweden 310 University of Malta (UM), Msida, Malta 311 University of Manchester (UMAN), Manchester, UK 312 University of Maryland (UMD), College Park, MD, USA 313 University of Massachusetts-Amherst (UMass), Amherst, MA, USA 314 University of Melbourne (UniMelb), Melbourne, Australia 315 University of Michigan (UMich), Ann Arbor, MI, USA 316 University of New Mexico (NMU), Albuquerque, NM, USA 317 University of Notre Dame du Lac (ND), South Bend, IA, USA 318 University of Oregon (UO), Eugene, OR, USA 319 University of Rochester (Rochester), Rochester, NY, USA 320 University of Rostock (U Rostock), Rostock, Germany 321 University of Saskatchewan (USASK), Saskatoon, Canada 322 University of Science and Technology of China (USTC), Hefei, P.R. China 323 University of Science and Technology of Mazandaran (USTM), Behshahr, Iran 324 University of Silesia (USKAT), Katowice, Poland 325 University of Stavanger (UiS), Stavanger, Norway 326 University of Stuttgart (USTUTT), Stuttgart, Germany 327 University of Sussex (US), Brighton, UK 328 University of the Witwatersrand (WITS), Johannesburg, South Africa 329 University of Toronto (UToronto), Toronto, Canada 330 University of Warsaw (UW), Warszawa, Poland 331 University of Wisconsin-Madison (WISC), Madison, WI, USA 332 University of Wurzburg (U Wurzburg), Wurzburg, Germany 333 University of Zurich (UZH), Zurich, Switzerland 334 University Rey Juan Carlos (URJC), Madrid, Spain 335 Univ. Lyon 1, CNRS/IN2P3, Institut de Physique Nucleaire de Lyon (CNRS/IN2P3/ IPNL), Lyon, France 336 Uppsala University (UU), Uppsala, Sweden 337 Usak University (Usak), Usak, Turkey 338 Vienna University of Economics and Business (WU), Vienna, Austria 339 Vinca Institute of Nuclear Sciences (Vinca), Belgrade, Serbia 340 Vrije Universiteit Brussel (VUB), Brussels, Belgium 341 Washington University (WUSTL), St. Louis, MO, USA 342 Weizmann Institute (Weizmann), Rehovot, Israel 343 Max-Planck-Institut fur Physik (MPP), Werner-Heisenberg-Institut, Munich, Germany 344 Westfälische Wilhelms-Universität Munster (WWU), Münster, Germany 345 West Pomeranian University of Technology (ZUT), Szczecin, Poland 346 Wroclaw University of Science and Technology (PWR), Wroclaw, Poland 347 Wuhan University of Technology (WHUT), Wuhan, P.R. China 348 Department of Physic (ZIMP), Zhejiang Institute of Modern Physics, Hangzhou, P.R. China 349 Zhejiang University (ZJU), Hangzhou, P.R. China 350 University of Colorado Boulder (CU Boulder), Boulder, CO, USA 351 Pittsburgh University (PITT), Pittsburgh, USA 352 fcc.secretariat@cern.ch Received 20 December 2018 Published online 10 June 2019 274 The European Physical Journal Special Topics Abstract. In response to the 2013 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) study was launched, as an international collaboration hosted by CERN. This study covers a highest-luminosity high-energy lepton collider (FCC- ee) and an energy-frontier hadron collider (FCC-hh), which could, successively, be installed in the same 100 km tunnel. The scientific capabilities of the integrated FCC programme would serve the world- wide community throughout the 21st century. The FCC study also investigates an LHC energy upgrade, using FCC-hh technology. This document constitutes the second volume of the FCC Conceptual De- sign Report, devoted to the electron-positron collider FCC-ee. After summarizing the physics discovery opportunities, it presents the ac- celerator design, performance reach, a staged operation scenario, the underlying technologies, civil engineering, technical infrastructure, and an implementation plan. FCC-ee can be built with today’s technology. Most of the FCC-ee infrastructure could be reused for FCC-hh. Com- bining concepts from past and present lepton colliders and adding a few novel elements, the FCC-ee design promises outstandingly high luminosity. This will make the FCC-ee a unique precision instrument to study the heaviest known particles (Z, W and H bosons and the top quark), offering great direct and indirect sensitivity to new physics. a e-mail: Michael.Benedikt@cern.ch FCC-ee: The Lepton Collider 275 Preface The 2013 Update of the European Strategy for Particle Physics (ESPPU) [1] stated, inter alia, that Europe needs to be in a position to propose an ambitious post- LHC accelerator project at CERN by the time of the next Strategy update” and that “CERN should undertake design studies for accelerator projects in a global context, with emphasis on proton-proton and electron-positron high-energy frontier machines. These design studies should be coupled to a vigorous accelerator R&D programme, including high-field magnets and high-gradient accelerating structures, in collaboration with national institutes, laboratories and universities worldwide”. In response to this recommendation, the Future Circular Collider (FCC) study was launched [2] as a world-wide international collaboration under the auspices of the European Committee for Future Accelerators (ECFA). The FCC study was mandated to deliver a Conceptual Design Report (CDR) in time for the following update of the European Strategy for Particle Physics. European studies of post-LHC circular energy-frontier accelerators at CERN had actually started a few years earlier, in 2010-2013, for both hadron [3-5] and lep- ton colliders [6-8], at the time called HE-LHC/VHE-LHC and LEP3/DLEP/TLEP, respectively. In response to the 2013 ESPPU, in early 2014 these efforts were com- bined and expanded into the FCC study. The 2013 ESPPU recognised the importance of electron-positron colliders for the precise measurement of the properties of the Higgs boson. Since its inception, the international FCC collaboration has worked on delivering the conceptual design for a staged e+ e- collider (FCC-ee) that would allow detailed studies of the heaviest known particles (Z, W and H bosons and the top quark) and offer great direct and indirect sensitivity to new physics. Five years of intense work and a steadily growing international collaboration have resulted in the present Conceptual Design Report, consisting of four volumes covering the physics opportunities, technical challenges, cost and schedule of several different circular colliders, some of which could be part of an integrated programme extending until the end of the 21st century. Geneva, December 2018 Rolf Heuer Fabiola Gianotti CERN Director-General 2009-2015 CERN Director-General since 2016 276 The European Physical Journal Special Topics Contents 1 Physics discovery potential ........................................................290 1.1 Overview ....................................................................290 1.2 Precision electroweak measurements...........................................293 1.2.1 Current situation....................................................293 1.2.2 Opportunities at the Z pole..........................................295 1.2.3 Opportunities at the W+ W- and tt threshold..........................298 1.2.4 Additional opportunities.............................................300 1.2.5 Global electroweak Fit...............................................301 1.3 The Higgs boson ............................................................ 303 1.3.1 Absolute coupling determination from the Higgs branching fractions .......................................................... 303 1.3.2 Additional opportunities.............................................306 1.4 Discovery potential for new physics ........................................ 309 1.4.1 Generic constraints on effective interactions from precision measurements ....................................................... 309 1.4.2 Sensitivity to new physics predicted in specific BSM models . . 313 1.5 Requirements ............................................................... 320 1.5.1 Collider ........................................................... 320 1.5.2 Detectors............................................................322 1.5.3 Theory ..............................................................323 2 Collider design and performance ................................................... 324 2.1 Requirements and design considerations ..................................... 324 2.2 Layout and key parameters ................................................ 324 2.2.1 Layout ............................................................. 324 2.2.2 Beam parameter optimisation ........................................ 326 2.3 Design challenges and approaches ......................................... 330 2.3.1 Synchrotron radiation .............................................. 330 2.3.2 Tapering ............................................................331 2.3.3 Dynamic aperture, beam lifetime, top-up injection .................. 331 2.3.4 Low emittance tuning and optics correction ......................... 331 2.4 Optics design and beam dynamics .......................................... 333 2.4.1 Lattices ........................................................... 333 2.4.2 Interaction region ................................................. 335 2.4.3 RF section and other straight sections...............................337 2.4.4 Dynamic aperture ................................................... 338 2.4.5 Tolerances and optics tuning ....................................... 342 2.4.6 Improving dynamic and momentum aperture using PSO and machine learning ................................................... 343 2.5 Machine detector interface ................................................. 346 2.5.1 Overall layout of the interaction region ........................... 346 2.5.2 Magnet systems ......................................................349 2.5.3 Luminometer..........................................................350 2.5.4 Synchrotron radiation .............................................. 350 2.5.5 Beamstrahlung, radiative bhabha scattering ......................... 352 2.6 Collective effects ......................................................... 353 2.6.1 Introduction ....................................................... 353 2.6.2 Impedance budget ................................................... 353 2.6.3 Resistive wall impedance ........................................... 353 2.6.4 RF cavities and tapers ............................................. 353 2.6.5 Synchrotron radiation absorbers .................................... 354 2.6.6 Collimators ........................................................ 354 FCC-ee: The Lepton Collider 277 2.6.7 Beam position monitors...............................................355 2.6.8 RF shielding ........................................................355 2.6.9 Overall impedance budget.............................................356 2.6.10 Single bunch instabilities ..........................................356 2.6.11 Microwave instability ...............................................357 2.6.12 Transverse mode-coupling instability.................................359 2.6.13 Multi-bunch instabilities............................................359 2.6.14 Bunch-by-bunch feedback..............................................360 2.6.15 Interaction region impedance budget .................................362 2.6.16 Electron cloud ......................................................363 2.6.17 Fast beam-ion instability ...........................................366 2.7 Energy calibration and polarisation...........................................368 2.8 Injection and extraction......................................................374 2.8.1 Top-up injection.....................................................374 2.8.2 Extraction and beam dump.............................................376 2.9 Operation and performance.....................................................376 2.9.1 Efficiency...........................................................376 2.9.2 Physics goals........................................................376 2.9.3 Estimated annual performance.........................................377 2.9.4 Radiofrequency system staging........................................378 2.9.5 Luminosity parameters and operation plan ............................379 2.9.6 Benchmarking against performance of past and present colliders379 2.10 Running at other energies.....................................................385 2.10.1 s-channel H Production...............................................385 2.10.2 Higher collision energy ............................................ 387 3 Collider technical systems ......................................................... 387 3.1 Introduction ................................................................ 387 3.2 Main magnet system .......................................................... 387 3.2.1 Introduction ....................................................... 387 3.2.2 Main dipole magnets ................................................ 388 3.2.3 Main quadrupole magnets ............................................ 390 3.2.4 Main sextupole magnets ............................................. 393 3.2.5 Main magnet powering ............................................... 393 3.2.6 Interaction region and final focus quadrupoles.......................395 3.2.7 Final-focus quadrupoles..............................................396 3.2.8 Final-focus sextupoles...............................................398 3.2.9 Polarisation wigglers................................................398 3.2.10 Magnets for the booster..............................................400 3.3 Vacuum system and electron-cloud mitigation...................................401 3.3.1 Introduction ........................................................401 3.3.2 Arc vacuum system ...................................................401 3.3.3 Interaction-region vacuum system ....................................405 3.3.4 Local beam-pipe shielding............................................406 3.4 Radiofrequency system.........................................................408 3.4.1 Overview.............................................................408 3.4.2 Superconducting cavities.............................................411 3.4.3 Powering ............................................................412 3.4.4 Feedback ............................................................414 3.4.5 Low-level RF ....................................................... 414 3.4.6 Staging..............................................................414 3.4.7 Beam-cavity interaction and beam dynamics issues ................... 416 3.5 Beam transfer systems.........................................................417 3.5.1 Introduction ........................................................418 278 The European Physical Journal Special Topics 3.5.2 Injection system......................................................418 3.5.3 Beam abort system.....................................................421 3.5.4 Parameter tables......................................................422 3.6 Beam diagnostics requirements and concepts ....................................422 3.6.1 Beam position monitoring..............................................425 3.6.2 Beam size monitoring..................................................425 3.6.3 Bunch length monitoring ..............................................426 3.6.4 Beam current and intensity measurements...............................426 3.6.5 Beam loss monitoring..................................................427 3.6.6 Topics for further study..............................................427 3.7 Combined polarimeter and spectrometer..........................................427 3.8 Halo collimators ..............................................................432 3.9 Machine protection.............................................................432 3.9.1 Architecture and powering of magnet circuits..........................432 3.9.2 Magnet protection and energy extraction ..............................432 3.9.3 Beam protection concepts..............................................433 3.10 Controls requirements and concepts ...........................................433 3.11 Radiation environment.........................................................435 3.11.1 Reference radiation levels ......................................... 435 3.11.2 Radiation hardness ................................................. 436 3.11.3 Radiation-hard technology trends ................................... 437 4 Civil engineering .................................................................. 439 4.1 Requirements and design considerations ....................................... 439 4.2 Layout and placement ......................................................... 439 4.2.1 Layout................................................................439 4.2.2 Placement.............................................................440 4.2.3 Necessary site investigations.........................................442 4.3 Underground structures.........................................................443 4.3.1 Tunnels...............................................................443 4.3.2 Shafts................................................................445 4.3.3 Alcoves...............................................................446 4.3.4 Experiment caverns ...................................................446 4.3.5 Service caverns.......................................................446 4.3.6 Junction caverns......................................................447 4.4 Surface sites..................................................................447 4.4.1 Experiment surface sites..............................................447 4.4.2 Technical surface sites...............................................447 4.4.3 Access roads .........................................................448 5 Technical infrastructure.............................................................448 5.1 Requirements and design considerations.........................................448 5.2 Piped utilities................................................................448 5.2.1 Introduction .........................................................448 5.2.2 Water cooling.........................................................449 5.2.3 Operational parameters................................................450 5.2.4 Chilled water.........................................................451 5.2.5 Drinking water........................................................452 5.2.6 Fire fighting network.................................................452 5.2.7 Reject water .........................................................452 5.2.8 Compressed air........................................................453 5.3 Heating, ventilation, air conditioning.........................................453 5.3.1 Overall design concept................................................453 5.3.2 Interior conditions...................................................453 5.3.3 Ventilation of underground areas......................................453 FCC-ee: The Lepton Collider 279 5.3.4 Machine tunnel.......................................................454 5.3.5 Experiment caverns ..................................................455 5.3.6 Other areas..........................................................455 5.3.7 Operating modes......................................................455 5.3.8 Working parameters...................................................456 5.3.9 Ventilation of surface buildings.....................................457 5.3.10 Safety..............................................................457 5.4 Electricity distribution ................................................... 458 5.4.1 Conceptual layout .................................................. 458 5.4.2 Source of electrical energy..........................................458 5.4.3 Transmission network topology ...................................... 458 5.4.4 Distribution network topology ...................................... 460 5.4.5 Power quality and transient voltage dip mitigation ................. 460 5.5 Emergency power..............................................................462 5.6 Cryogenic system.............................................................464 5.6.1 Overview.............................................................464 5.6.2 Functions and constraints .......................................... 464 5.6.3 Layout and architecture ............................................ 465 5.6.4 Temperature levels ................................................. 466 5.6.5 Heat loads ......................................................... 467 5.6.6 Cooling scheme and cryogenic distribution .......................... 467 5.6.7 Cryogenic plants ................................................... 468 5.6.8 Cryogen inventory and storage ...................................... 469 5.7 Equipment transport and handling ........................................... 469 5.7.1 Underground vehicles ............................................... 469 5.7.2 Overhead cranes .................................................... 470 5.7.3 Lifts................................................................472 5.8 Personnel transport ........................................................ 473 5.8.1 Transport for emergency services ................................... 473 5.9 Geodesy, survey and alignment .............................................. 474 5.9.1 Introduction ........................................................474 5.9.2 Alignment tolerances ............................................... 474 5.9.3 Geodesy ............................................................ 475 5.9.4 Metrological aspects ............................................... 475 5.9.5 Alignment of accelerator components ................................ 476 5.9.6 Interaction regions and collimator areas ........................... 477 5.9.7 Experiments ........................................................ 477 5.10 Communications, computing and data services ............................... 477 5.11 Safety and access management systems ...................................... 481 6 Injector complex .................................................................. 482 6.1 Injector overview .......................................................... 482 6.2 Electron gun ............................................................... 484 6.3 Linac ...................................................................... 484 6.4 Linac at 20GeV ..............................................................487 6.5 Positron source and capture system ......................................... 488 6.6 Damping ring ............................................................... 490 6.7 Bunch compressors .......................................................... 492 6.8 Pre-booster ................................................................ 493 6.9 Booster .................................................................... 494 6.10 Transfer lines..............................................................496 7 Experiment environment and detector designs ....................................... 497 7.1 Experiment environment ..................................................... 497 7.1.1 Synchrotron radiation .............................................. 497 280 The European Physical Journal Special Topics 7.1.2 Pair-production background ........................................ 499 7.2 Luminometer .............................................................. 499 7.2.1 Design..............................................................500 7.2.2 Acceptance and luminosity measurement ............................. 502 7.2.3 Electromagnetic focussing of bhabha electrons ..................... 503 7.2.4 Machine and beam-induced backgrounds in the luminometer . 503 7.3 The CLD detector design .................................................. 504 7.3.1 CLD tracking system ............................................... 504 7.3.2 Backgrounds in the CLD tracking system ............................ 506 7.3.3 CLD calorimetry ................................................... 507 7.3.4 CLD Muon system ................................................... 507 7.4 IDEA detector concept .................................................... 508 7.4.1 IDEA vertex detector ...............................................508 7.4.2 IDEA drift chamber..................................................509 7.4.3 IDEA tracking system performance....................................510 7.4.4 Backgrounds in the IDEA tracking system.............................510 7.4.5 IDEA preshower detector.............................................511 7.4.6 IDEA dual-readout calorimeter.......................................512 7.4.7 IDEA muon system ...................................................513 7.5 Detector magnet systems .................................................. 513 7.5.1 The CLD detector magnet.............................................513 7.5.2 The IDEA Detector Magnet............................................513 7.6 Constraints on readout systems..............................................515 7.7 Infrastructure requirements .............................................. 516 8 Safety..........................................................................517 8.1 Safety policy and regulatory framework .....................................517 8.1.1 Legal context of CERN ..............................................517 8.1.2 Hazard register and safety performance based design ............... 517 8.2 Occupational health and safety.............................................518 8.2.1 Fire hazard.........................................................518 8.2.2 Oxygen deficiency...................................................520 8.3 Radiation protection.......................................................520 8.3.1 Particle beam operation.............................................521 8.3.2 Activation of solids................................................521 8.3.3 Activated or contaminated liquids ..................................522 8.3.4 Activated or radioactive gases and radioactive aerosols.............522 9 Energy efficiency...............................................................522 9.1 Requirements and design considerations.....................................522 9.2 Power requirements.........................................................523 9.3 Energy management and saving...............................................525 9.4 Waste heat recovery......................................................526 10 Environment .....................................................................528 10.1 Requirements and approach considerations ................................ 528 10.1.1 Legal context.......................................................528 10.1.2 Environmental compatibility management concept......................529 10.2 Environmental impact .................................................... 530 10.2.1 Radiological impact ................................................530 10.2.2 Conventional impact.................................................531 10.3 Waste management ........................................................ 532 10.3.1 Radioactive waste management........................................532 10.3.2 Conventional waste management.......................................533 11 Education, economy and society ................................................ 534 11.1 Implementation with the host states ................................... 534 FCC-ee: The Lepton Collider 281 11.1.1 Overview............................................................534 11.1.2 France ............................................................ 536 11.1.3 Switzerland ....................................................... 538 11.2 Socio-economic opportunities ............................................ 539 11.2.1 Introduction and motivation ....................................... 539 11.2.2 The value of training ............................................. 540 11.2.3 Opportunities for industries and technological spillover............541 11.2.4 Cultural effects....................................................544 11.2.5 Impact potential .................................................. 546 12 Strategic research and development..............................................547 12.1 Introduction...............................................................547 12.2 High efficiency radiofrequency power sources..............................548 12.3 High efficiency superconducting radiofrequency cavities...................549 12.4 Energy storage and release R&D............................................551 12.5 Efficient power distribution infrastructure ............................. 553 12.6 Efficient use of excavation materials ................................... 555 Appendix A: Theoretical physics computations........................................559 Appendix B: Uncertainties ..........................................................561 B.1 Accelerator and technologies................................................561 B.2 Implementation .............................................................564 Appendix C: Communities ........................................................... 567 Appendix D: Timeline .............................................................. 570 Appendix E: Costs ................................................................. 571 E.1 Construction costs ........................................................ 571 E.2 Operation costs ........................................................... 571 Executive summary Overview Particle physics has arrived at an important moment in its history. The discovery of the 125 GeV Higgs boson completes the matrix of particles and interactions that has constituted the “Standard Model” for several decades. This model is a con- sistent and predictive theory, which has so far proven successful at describing all phenomena accessible to collider experiments. On the other hand, several exper- imental facts require the extension of the Standard Model and explanations are needed for observations such as the domination of matter over antimatter, the evi- dence for dark matter and the non-zero neutrino masses. Theoretical issues that need to be addressed include the hierarchy problem, the neutrality of the Universe, the stability of the Higgs boson mass upon quantum corrections and the strong CP problem. This report contains the description of a novel research infrastructure based on a highest-luminosity energy frontier electron-positron collider (FCC-ee) to address the open questions of modern physics. It will be a general precision instrument for the continued in-depth exploration of nature at the smallest scales, optimised to study with high precision the Z, W, Higgs and top particles, with samples of 5 x 1012 Z bosons, 108 W pairs, 106 Higgs bosons and 106 top quark pairs. The FCC-ee offers unprecedented sensitivity to signs of new physics, appearing in the form of small deviations from the Standard Model, of forbidden decay processes, or of production of new particles with very small couplings. This collider will be implemented in stages, successively spanning the entire energy range from the Z pole over the WW threshold and HZ production peak 282 The European Physical Journal Special Topics Fig. 1. Overall layout of the FCC-ee with a zoomed view of the trajectories across inter- action point G. The FCC-ee rings are placed 1 m outside the FCC-hh footprint (used for the booster and indicated in green colour in the figure) in the arc. In the arc the e+ and e- rings are horizontally separated by 30 cm. The main booster follows the footprint of the FCC-hh collider ring. The interaction points are shifted by 10.6 m towards the outside of FCC-hh. The beam trajectories toward the IP are straighter than the outgoing ones in order to reduce the synchrotron radiation at the IP. to the tt threshold and above. Most of the infrastructure (e.g. underground struc- tures, surface sites, electrical distribution, cooling & ventilation, RF systems) can be directly reused for a subsequent highest-energy hadron collider (described in the FCC Conceptual Design Report volume 3). The complex will thus serve the world- wide particle-physics community in a highly synergetic and cost-effective manner throughout the 21st century. The European Strategy for Particle Physics (ESPP) 2013 update stated “To stay at the forefront of particle physics, Europe needs to be in a position to propose an ambitious post-LHC accelerator project at CERN by the time of the next Strategy update”. The FCC study has implemented the ESPP recommendation by developing a long-term vision for an “accelerator project in a global context”. This document describes the detailed design and preparation of a construction project for a post- LHC circular lepton collider “in collaboration with national institutes, laboratories and universities worldwide”, and enhanced by a strong participation of industrial partners. A coordinated preparation effort can now be based on a core of an ever- growing consortium of already more than 135 institutes world-wide. FCC-ee: The Lepton Collider 283 Table 1. Machine parameters of the FCC-ee for different beam energies. Z 1 WW 1 ZH 1 tt Circumference (km) Bending radius (km) Free length to IP l * (m) Solenoid field at IP (T) Full crossing angle at IP 6 (mrad) SR power/beam (MW) 97.756 10.760 2.2 2.0 30 50 Beam energy (GeV) 45.6 80 120 175 182.5 Beam current (mA) 1390 147 29 6.4 5.4 Bunches/beam 16 640 2000 328 59 48 Average bunch spacing (ns) 19.6 163 994 2763 3396 Bunch population (1011) 1.7 1.5 1.8 2.2 2.3 Horizontal emittance ex (nm) Vertical emittance ey (pm) 0.27 1.0 0.84 1.7 0.63 1.3 1.34 2.7 1.46 2.9 Horizontal ß* (m) Vertical ß* (mm) 0.15 0.8 0.2 1.0 0.3 1.0 1.0 1.6 Energy spread (SR/BS) as (%) 0.038/0.132 0.066/0.131 0.099/0.165 0.144/0.186 0.150/0.192 Bunch length (SR/BS) az (mm) 3.5/12.1 3.0/6.0 3.15/5.3 2.01/2.62 1.97/2.54 Piwinski angle (SR/BS) ß 8.2/28.5 3.5/7.0 3.4/5.8 0.8/1.1 0.8/1.0 Energy loss/turn (GeV) 0.036 0.34 1.72 7.8 9.2 RF frequency (MHz) 400 400/800 RF voltage (GV) 0.1 0.75 2.0 4.0/5.4 4.0/6.9 Longitudinal damping time (turns) 1273 236 70.3 23.1 20.4 Energy acceptance (DA) (%) ±1.3 ±1.3 ±1.7 -2.8 +2.4 Polarisation time tp (min) 15000 900 120 18.0 14.6 Luminosity/IP (1034/cm2s) 230 28 8.5 1.8 1.55 Beam-beam £x/£y 0.004/0.133 0.010/0.113 0.016/0.118 0.097/0.128 0.099/0.126 Beam lifetime by rad. Bhabha scattering (min) 68 59 38 40 39 Actual lifetime incl. beam- strahlung (min) >200 >200 18 24 18 Notes. For tt operation a common RF system is used. Accelerator The FCC-ee accelerator design provides a high luminosity at each of many different collision energies, between 88 and 365 GeV, while satisfying several stringent con- straints. Apart from a ±1.2km-long section around each interaction point (IP), the machine follows the layout of the 97.75 km circumference hadron collider [9]. The present design houses two interaction points. The synchrotron radiation power is limited to 50 MW per beam at all energies. 284 The European Physical Journal Special Topics Machine design and layout For a collision energy of 365 GeV, as required for tt operation, the cost-optimised circumference is about 100 km [10]. The FCC-ee is designed as a double ring col- lider, like the KEKB and PEP-II B factories. The double-ring configuration allows a large number of bunches (Fig. 1 shows the layout). The two beam lines cross at two interaction points (IPs) with a horizontal crossing angle of 30 mrad. Profiting from the crossing angle, a crab waist collision scheme [11,12] is adopted, which enables an extremely small vertical beta function ß* at the IP (about 50 times smaller than at LEP) and a high beam-beam tune shift. This novel collision scheme has been successfully used at DA$NE since 2008/09. The critical energy of the synchrotron radiation of the incoming beams towards the IP is kept below 100 keV at all beam energies. A common lattice is used for all beam energies, except for a small rear- rangement in the RF section for the tt mode. The betatron tune, phase advance in the arc cell, final focus optics and the configuration of the sextupoles are set to the optimum at each energy by changing the strengths of the magnets. The two experiments are situated in points A and G. The length of the free area around the IP (I*) and the strength of the detector solenoid are kept constant at 2.2 m and 2T, respectively, for all energies. A “tapering” scheme scales the strengths of all magnets, apart from the solenoids, according to the local beam energy, taking into account the energy loss due to synchrotron radiation. Two RF sections per ring are placed in the straight sections at points D and J. The RF cavities will be common to e+ and e- in the case of tt. Parameters The FCC-ee machine parameters are compiled in Table 1. The beam current varies greatly between the Z pole and the tt threshold. The current is adjusted primarily by changing the number of bunches. In present electron storage rings, the equilibrium beam parameters are determined by synchrotron radiation (SR) generated in the dipoles of the collider arcs. For the FCC-ee, the energy spread and the beam lifetime are also affected by beamstrahlung (BS), which is a special type of synchrotron radiation, emitted during the collision due to the field of the opposite bunch. Injection A top-up injection scheme maintains the stored beam current and the luminosity at the highest level throughout the physics run. Without top-up injection the inte- grated luminosity would be more than an order of magnitude lower. It is, therefore, necessary to install a booster synchrotron in the collider tunnel. Injection into the top-up booster takes place at 20 GeV, similar to injection into LEP. The layout of the pre-injector complex resembles the KEKB/SuperKEKB injector. For the FCC-ee, it consists of a 6 GeV normal-conducting S-band linac, a prebooster (possibly the SPS) which accelerates the electron and positron beams from 6 to 20 GeV, a positron source, where 4.46 GeV electrons from the linac are sent onto a hybrid target with flux concentrator, and a small positron damping ring. The linac will accelerate 1 or 2 bunches per pulse at a repetition rate of 100 or 200 Hz. The complete filling for Z running is the most demanding with respect to the number of bunches, bunch intensity and therefore injector flux. It requires a linac bunch intensity of 2 x 1010 particles for both species. The positron rate required is similar to the rates at SuperKEKB and the SLC. Alternative injector scenarios could include a longer 20 GeV linac, without any pre-booster, or a recirculating SC linac. FCC-ee: The Lepton Collider 285 Fig. 2. Baseline luminosities expected to be delivered (summed over all interaction points) as a function of the centre-of-mass energy y/s, at each of the four worldwide e+e- collider projects: ILC (blue square), CLIC (green upward triangles), CEPC (black downward trian- gles), and FCC-ee (red dots), drawn with a 10% safety margin. The FCC-ee performance data are taken from this volume, the latest incarnation of the CEPC parameters is inferred from [20], and the linear collider luminosities are taken from [15,17]. Performance As a result of the renewed worldwide interest for e+e- physics and the pertaining discovery potential since the observation of the Higgs boson at the LHC, the FCC is not alone in its quest. Today four e+e- collider designs are contemplated to study the properties of the Higgs boson and other standard model (SM) particles with an unprecedented precision: the International Linear Collider (ILC [13]) project with a centre-of-mass energy of 250 GeV [14,15]; the Compact Linear Collider (CLIC [16]), whose lowest centre-of-mass energy point was reduced from 500 to 380 GeV [17]; the Circular Electron Positron Collider (CEPC [18-20]), in a 100km tunnel in China, with centre-of-mass energies from 90 to 250 GeV; and the Future e+e- Circular Collider in a new ^100km tunnel at CERN (FCC-ee, formerly called TLEP [8,21]). The baseline luminosities expected to be delivered at the ILC, CLIC, CEPC, and FCC-ee centre-of-mass energies are illustrated in Figure 2. The expected integrated luminosities and operation phases at each energy are illustrated in Figure 3. The FCC-ee delivers the highest rates in a clean, well- defined, and precisely predictable environment, at the Z pole (91 GeV), at the WW threshold (161 GeV), as a Higgs factory (240 GeV), and around the tt thresh- old (340-365GeV), to two interaction points. Thanks to the availability of trans- verse polarisation up to over 80 GeV beam energy, it also provides high precision centre-of-mass energy calibration at the 100 keV level at the Z and W energies, a unique feature of circular colliders. The FCC-ee is, therefore, genuinely best suited to offer extreme statistical precision and experimental accuracy for the measure- ments of the standard model particle properties, it opens windows to detect new rare processes, and it furnishes opportunities to observe tiny violations of established symmetries. 286 The European Physical Journal Special Topics Fig. 3. Operation model for the FCC-ee, resulting from the five year conceptual design study, showing the integrated luminosity at the Z pole (black), the WW threshold (blue), the Higgs factory (red), and the top-pair threshold (green) as a function of time. The hatched area indicates the shutdown time needed to prepare the collider for the highest energy runs. Fig. 4. FCC-ee operation time line. The bottom part indicates the number of cryomodules to be installed in the collider and booster, respectively, during the various winter shutdown periods; also see [22]. Technical systems Table 1 reveals that the FCC-ee machine faces quite different requirements in its various modes of operation. For example, on the Z pole FCC-ee is an Ampere-class storage ring, like PEP-II, KEKB and DA$NE, with a high beam current, but a low RF voltage, of order 0.1 GV. For the tt mode, the beam current is only a few mA, as for the former LEP2, while an RF voltage above 10 GV is required. In both cases a total of 100 MW RF power must be constantly supplied to the two circulating beams. Three sets of RF cavities are proposed to cover all operation modes for the FCC-ee collider rings and booster. (1) For the high intensity operation (Z, FCC-hh) 400 MHz mono-cell cavities (4 per cryomodule) based on Nb/Cu thin-film technol- ogy at 4.5 K; (2) for higher energy (W, H, tt) 400 MHz four-cell cavities (4 per cryomodule) again based on Nb/Cu technology at 4.5K, and (3), finally for the tt machine a complement of 800 MHz five-cell cavities (again 4 per cryomodule) based on bulk Nb at 2 K. The installation sequence (Fig. 4) is comparable to that of LEP, where about 30 cryomodules were installed per shutdown. A high overall energy efficiency is achieved through a combination of dif- ferent technical and operational measures, for example, by using advanced RF FCC-ee: The Lepton Collider 287 Fig. 5. Left: 3D, not-to-scale schematic of the underground structures. Right: study bound- ary (red polygon), showing the main topographical and geological structures, LHC (blue line) and FCC tunnel trace (brown line). power sources [23] and novel low-power twin aperture magnets [24], and by top-up injection. Civil engineering The principal structure of the FCC-ee collider is a quasi-circular tunnel composed of arc segments interleaved with straight sections with 5.5 m diameter and a cir- cumference of 97.75 km. Approximately 8 km of bypass tunnels, 18 shafts, 14 large caverns and 12 new surface sites are also planned. On the left, Figure 5 shows a 3D, not-to-scale schematic of the underground structures. The chosen layout satisfies the requirements of the FCC-ee and the FCC-hh machine. Many different considerations played a role in choosing a suitable position for the machine. The underground structures should be located as much as possible in the sedimentary rock of the Geneva basin, known as Molasse (which provides good conditions for tunneling) avoiding the limestone of the nearby Jura. Another aim was to limit the depth of the tunnel and shafts to control the overburden pressure on the underground structures and to limit the lengths of service infrastructures (cables, ducts, pipes). These requirements, along with the need to connect to the existing accelerator chain through new beam transfer lines, led to the definition of the study boundary, within the Jura range to the north-west, the Vuache mountain to the south-west and the Pre-Alps to the south-east and east. An additional boundary is placed to the north due to the increasing depth of Lake Geneva (see Fig. 5 right). In order to evaluate different layouts and positions within the boundary area, a software tool incorporating a 3D geological model was developed and used. The tunnel will be constructed with a slope of 0.2% in a single plane, in part to opti- mise for the geology intersected by the tunnel and the shaft depths and in part to implement a gravity drainage system. It is anticipated that the majority of the machine tunnel will be constructed using tunnel boring machines. One sector pass- ing through limestone will be mined. For the excavations, different lining designs have been developed corresponding to the rock condition. The study was based on geological data from previous projects and data available from national services. Based on this information, the civil engineering project is considered feasible, both in terms of technology and project risk control. Dedicated 288 The European Physical Journal Special Topics Fig. 6. Machine tunnel cross section in a regular arc with machine elements, services and transport equipment. ground and site investigations are required during the early stage of a preparatory phase to confirm the findings and to provide a comprehensive technical basis for an optimised placement and as preparation for project planning and implementation processes. For the access points and their associated surface structures, the focus was iden- tifying possible locations which are feasible from socio-urbanistic and environmental perspectives. The construction methods, and hence the technical feasibility of con- struction, were studied and are deemed achievable. A 5.5 m internal diameter tunnel is required to house all necessary equipment for the machine, while providing sufficient space for transport. The chosen diameter is also compatible with the FCC-hh requirements. Figure 6 shows the cross section of the tunnel in a typical arc segment, with air supply and smoke extraction ducts integrated into the civil engineering design, the collider and the booster ring as well as the other services required. Detector considerations Circular colliders have the advantage of delivering collisions to multiple interac- tion points. Several experimental collaborations will therefore be called to study and optimise different detector designs for the FCC-ee. On one hand, the planned performance of these detectors for heavy-flavour tagging, for particle identification, for tracking and particle-flow reconstruction, and for lepton, jet, missing energy and angular resolution, need to match the physics programme and the statistical precision offered by the FCC-ee. On the other hand, the detectors must satisfy the constraints imposed by machine performance and interaction region layout: the occu- pancy from beam-induced background needs to be minimised; the interaction rates (up to 100 kHz at the Z pole) put strict constraints on the event size and readout speed; due to the beam crossing angle, the detector solenoid magnetic field is limited to 2 T to avoid a significant impact on the luminosity; the accurate measurement of the significant centre-of-mass energy spread (90 MeV at the Z pole, 500 MeV at the highest FCC-ee energies) requires an angular resolution better than 100 p,rad for FCC-ee: The Lepton Collider 289 muons; the luminometer must be situated only 1 m away from the interaction point, but still provide a precision better than 10-4 on the luminosity; etc. Two general-purpose detector concepts have been studied and optimised for this conceptual design report: (i) CLD, a consolidated option based on the detector design developed for CLIC, with a silicon tracker and a 3D-imaging highly-granular calorimeter, surrounded by a conventional superconducting solenoid coil; and (ii) IDEA, a bolder, possibly more cost-effective, design, with a short-drift wire chamber and a dual-readout calorimeter, interleaved by a thin, low-mass supercon- ducting solenoid coil. This particular choice has been motivated by the wish to explore the technology and cost spectrum. With these two examples, it was demon- strated that detectors satisfying the requirements are feasible. This choice is of course not unique. While the optimisation of these two concepts will continue, other concepts must be explored and might actually prove to be better adapted to the FCC-ee physics programme. Cost and schedule The construction cost for FCC-ee amounts to 10 500 million CHF for the Z, W and H working points including all civil engineering works. All particle accelerator related investments amount to 3100 million CHF or 30% of the total cost and the staged implementation distributes these costs over a decade long operation phase. Civil engineering accounts for 51% (5400 million CHF). The capital cost for the technical infrastructure is 2000 million CHF. Both, civil engineering and general technical infrastructures can be fully reused for a subsequent hadron collider (FCC- hh). The operation costs are expected to remain within limits, since the electricity consumption is not a cost driver and the evolution from LEP to LHC operation today shows a steady decrease in the efforts needed to operate, maintain and repair the equipment. The cost-benefit analysis of the LHC/HL-LHC programme reveals that a research infrastructure project of such a scale and investment volume has the potential to pay back in terms of socio-economic value creation throughout its lifetime. The FCC-ee programme will commence with a preparatory phase of 8 years, followed by the construction phase (all civil and technical infrastructure, machines and detectors including commissioning) lasting 10 years. A duration of 15 years is projected for the subsequent operation of the FCC-ee facility, to complete the currently envisaged physics programme. This makes a total of nearly 35 years for construction and operation of FCC-ee. Outlook The technology for constructing a high-energy, highest-luminosity circular lepton collider exists today. The FCC-ee concept comprises a high-efficiency, supercon- ducting radiofrequency system, a power-saving twin-aperture magnet system, a continuous top-up injection scheme for stable operation and maximum integrated luminosity. Combined with an energy staging scheme, the FCC-ee represents the most efficient and most sustainable route for executing the research required to discover signs of new physics beyond the Standard Model. The step-wise energy increase of the FCC-ee does not require any additional civil engineering activities. Strategic R&D for FCC-ee aims at minimising construction cost and energy consumption, while maximising the socio-economic impact. It will mitigate resid- ual technology-related risks and ensure that industry can benefit from an accept- able economic utility. Concerning the implementation, a preparatory phase of about 290 The European Physical Journal Special Topics eight years is both necessary and adequate to establish the project governing and organisational structures, building the international machine and experiment con- sortia, developing a territorial implementation plan in agreement with the host states’ requirements, optimising the disposal of land and underground volumes and preparing the civil engineering project. Such a large-scale, international fundamental research infrastructure, tightly involving industrial partners and providing training at all education levels, will be a strong motor of economic and societal development in all participating nations. The FCC study has implemented a set of actions towards a coherent vision for the world-wide high-energy and particle physics community, providing a col- laborative framework for topically complementary and geographically well-balanced contributions. This conceptual design report lays the foundation for a subsequent infrastructure preparatory and technical design phase. 1 Physics discovery potential 1.1 Overview “There is a strong scientific case for an electron-positron collider, complemen- tary to the LHC, that can study the properties of the Higgs boson and other particles with unprecedented precision and whose energy can be upgraded.” [25] This strategic guideline from the 2013 update of the European Strategy for Particle Physics (ESPP 2013) unambiguously defines the high standards to be met by the future e+e- collider, quite possibly the next high-energy collider to be built. Since its inception, the FCC-ee study has aimed at delivering the e+e- collider conceptual design that best complies with this guideline, and consequently offers, in a cost-effective fashion, the broadest physics discovery potential and the most ambitious perspectives for future developments. As a result of the renewed worldwide interest for e+e- physics and the pertaining discovery potential since the observation of the Higgs boson at the LHC, the FCC is not alone in this quest. In the absence of convincing hints for physics beyond the standard model (BSM) in the LHC data so far, the situation has significantly evolved since 2013, so that today no fewer than four e+e- collider designs are contemplated to study the properties of the Higgs boson and other standard model (SM) particles with an unprecedented precision: — the International Linear Collider (ILC [13]) project, for which the above guideline was originally tailored, now focusses on studying the Higgs boson with a centre- of-mass energy of 250 GeV [14,15]; — the Compact Linear Collider (CLIC [16]), whose lowest centre-of-mass energy point was reduced from 500 to 380 GeV [17], in order to better study the Higgs boson and the top quark; — the Circular Electron Positron Collider (CEPC [18-20]), in a 100km tunnel in China, able to study the Z, the W, and the Higgs boson, with centre-of-mass energies from 90 to 250 GeV; — the Future e+e- Circular Collider in a new ^100 km tunnel at CERN (FCC-ee, formerly called TLEP [8,21]), which can study the entire electroweak (EW) sector (Z and W bosons, Higgs boson, top quark) with centre-of-mass energies between 88 and 365 GeV. The baseline luminosities expected to be delivered at the ILC, CLIC, CEPC, and FCC-ee centre-of-mass energies are illustrated in Figure 1.1. FCC-ee: The Lepton Collider 291 Fig. 1.1. Baseline luminosities expected to be delivered (summed overall interaction points) as a function of the centre-of-mass energy y/s, at each of the four worldwide e+e- collider projects: ILC (blue square), CLIC (green upward triangles), CEPC (black downward trian- gles), and FCC-ee (red dots), drawn with a 10% safety margin. The FCC-ee performance data are taken from Section 2, the latest CEPC parameters are taken from [20], and the linear collider luminosities are taken from [15,17]. The FCC-ee delivers the highest rates in a clean, well-defined, and precisely pre- dictable environment, at the Z pole (91 GeV), at the WW threshold (161 GeV), as a Higgs factory (240GeV), and around the tt threshold (340-365 GeV), to several interaction points. It also provides high precision centre-of-mass energy calibration at the 100 keV level at the Z and WW energies, a feature unique to circular col- liders1. The FCC-ee is therefore genuinely best suited to offer extreme statistical precision and experimental accuracy for the measurements of the standard model particle properties, it opens windows to detect new rare processes, and it furnishes opportunities to observe tiny violations of established symmetries. Historically, such precise measurements or subtle observations have been pre- cursors for the discovery of new phenomena and new particles, and for a deeper understanding of fundamental physics. These historical precedents have also shown the important role played by lower-energy precision measurements when establish- ing road-maps for higher-energy machines. In the second half of the 1970s, precision measurements of neutral currents led scientists to infer the existence of the W and Z bosons, as well as the values of their masses, from which the dimensions of the LEP tunnel were determined. The W and Z were then observed in the early 1980’s at the 1 A circular e+e- Higgs factory, LEP3, had also been proposed in the LHC tunnel back in 2011 [21,26]. With respect to the FCC-ee, the LEP3 facility would have had the advantage of reusing existing infrastructure, at the severe expense of a much reduced sensitivity to new phenomena, with (i) a luminosity smaller by a factor 4-5 at the Z, WW, and Higgs operation points; (ii) the impossibility of a precise energy calibration at the WW threshold; (iii) the inability to measure the top-quark properties; and (iv) the lack of a vibrant perspective for subsequent energy-frontier exploration in the same tunnel. 292 The European Physical Journal Special Topics Fig. 1.2. Operation model for the FCC-ee, as a result of the five-year conceptual design study, showing the integrated luminosity at the Z pole (black), the WW threshold (blue), the Higgs factory (red), and the top-pair threshold (green) as a function of time. The hatched area indicates the shutdown time needed to prepare the collider for the highest energy runs. CERN SppS collider with masses in the predicted range. Subsequently, as described in more detail in Section 1.2, the CERN LEP e+e- collider measured the properties of the Z and W bosons with high precision in the 1990’s [27,28]. These precise mea- surements could determine in a definitive way the number of light, active neutrinos, as well as allow inferring the mass of the so far unseen top quark, which was soon observed at the Tevatron within the predicted mass range. With mtop fixed by the Tevatron measurement, the ensemble of precision measurements at LEP/SLC, at the Tevatron, and from low energy inputs led in turn to a ±30% accurate prediction for the mass of the Higgs boson, which was observed in 2012 at the LHC within the predicted mass range. It is important to note that these predictions were based on the Standard Model with no additional particle content with respect to that known today. With the Higgs boson discovery, the standard model seems complete and its predictions have no more flexibility beyond the uncertainties in the theoretical cal- culations and in the input parameters. Several experimental facts, however, reveal without any doubt that new phenomena must exist: non-baryonic dark matter; the cosmological baryon-antibaryon asymmetry; the finite albeit extremely small neu- trino masses, etc., are all evidence for physics beyond the standard model. The agreement between the predicted and observed W, top and Higgs masses, and the null result of experiments at colliders so far, are an indication that either the new physics scale is too high and/or the pertaining couplings are too small. Any new hint would be a major discovery, whether it is the observation of a new particle, a new so-far unobserved phenomenon, or a non-trivial deviation from the standard model predictions. As a result, the next accelerator project must allow the broadest possible field of research. This is the case for the FCC. To begin with, the FCC-ee would measure the Z, W, Higgs, and top properties in e+e- collisions, either for the first time FCC-ee: The Lepton Collider 293 or with orders of magnitude increases in precision, thereby giving access to either much higher scales or much smaller couplings. The FCC-ee is the most powerful of all proposed e+e- colliders at the electroweak (EW) scale - all things being equal, in particular the duration of operation (Fig. 1.2). The FCC-ee proposes a broad, multifaceted exploration to 1. measure a comprehensive set of electroweak and Higgs observables with high precision, 2. tightly constrain a large number of the parameters of the standard model, 3. unveil small but significant deviations with respect to the standard model predic- tions, 4. observe rare new processes or particles, beyond the standard model expectations, and, therefore, maximise opportunities for major fundamental discoveries. The FCC- ee also meets the last part of the ESPP 2013 guideline (“[... ] and whose energy can be upgraded’) in the most ambitious manner, as the FCC-ee tunnel is designed to subsequently host the FCC-hh, a hadron collider with a centre-of-mass energy of 100 TeV. Combined with the FCC-ee measurements, the FCC-hh physics reach at the energy and precision frontiers is likely to be unbeatable. The multiple synergies between the FCC-ee and FCC-hh physics opportunities are discussed in Vol. 1 of this Conceptual Design Report. The primary goal of the FCC-ee design study was to demonstrate the feasibility of the accelerator. This goal has been successfully met, confirming and even exceeding the original luminosity expectations (Figs. 1.1 and 1.2). Great confidence can be given in the integration of the detectors at the collision points, and in the ability to reach the beam energy calibration targets. The exploration of the physics capabilities is still at a preliminary stage. Nevertheless the studies presented in the next sections provide a flavour of the extraordinary physics potential of the FCC-ee. 1.2 Precision electroweak measurements Since the early work by Veltman [29], it has been known that the electroweak quan- tum corrections are sensitive to particles with electroweak couplings and with masses much higher than accessible directly with the centre-of-mass energies available. The case of the top quark and Higgs boson were particularly interesting: despite their high masses, their effect would indeed not decouple. Further studies in the late 1980s led to the realisation that these quantum corrections could be separated into blocks with different sensitivities. Accurate measurements of these observables thus become sensitive to the possible presence of further particles coupled to the SM interactions in a broader sense. The FCC-ee enables precision measurements of the Z, the W, the Higgs boson and the top quark properties, together with those of input parameters to the standard model, such as the electromagnetic and strong coupling constants at the Z mass scale, thereby providing sensitivity to new particles with masses of up to 10-70 TeV. 1.2.1 Current situation As briefly mentioned above, the Z lineshape parameters (the Z mass mZ, the Z width rZ, and the peak cross section a0) fitted to the per-mil precision measurements of fermion pair production cross sections at and around the Z pole [27] performed at LEP, were sensitive to the yet unobserved top quark and to a lesser extent to the putative Higgs boson, as illustrated in the Feynman diagrams of Figure 1.3. 294 The European Physical Journal Special Topics Fig. 1.3. Schematic representation of the perturbative expansion for calculating the cross section for e+e- annihilation into a pair of leptons or quarks (denoted f, for fermions); the representative higher order diagrams involving quantum loops with a top quark or a Higgs boson are indicated. Similarly, the measurements of fermion pair asymmetries allow the determination of the effective weak mixing angle sin2 öW, the value of which is predicted in the SM from the relation: (1.1) where «QED(m|) is the electromagnetic coupling constant evaluated at the Z pole, GF is the Fermi constant, and Ak is a small correction factor that depends on the top quark and Higgs boson masses via the graphs displayed in Figure 1.3. The magnitude of the second graph of Figure 1.3 is proportional to the square of the top quark mass. It is much larger than that of the third one, proportional to log(mH/mZ), and amounts to about ten times the LEP measurement accuracy. As a consequence, LEP was able to predict the mass of the top quark within the SM (assuming that no other particle but the Higgs boson would impact the radiative corrections) [27]: (1.2) The W boson mass is in turn predicted within the SM from the relation: (1.3) where Ar is yet another small correction factor that depends on mtop and mH. Numerically, the W mass was predicted from the LEP measurements at the Z pole with a remarkable precision (including the above uncertainty on the top quark mass and the absence of knowledge of the Higgs boson at the time) [27]: (1.4) By increasing its centre-of-mass energy to above the W+W- production thresh- old, LEP did measure the W mass directly, in agreement with equation (1.4) and with a similar precision [28]. The Tevatron later improved this precision by about a factor two [30], and observed for the first time the top quark [31,32], at the mass predicted by LEP (Eq. (1.2)) in the context of the standard model and nothing else. Today, the W boson and top quark masses are directly measured with the following accuracies [33]: (1.5) (1.6) The direct measurements of mW and mtop were then used to determine the magnitude of the second graph of Figure 1.3, and made the third graph become the sin2 cos2 öW = nQgD(m2Z) X (1 + Ak), V2Gp mZ mtSoM = 173-10 GeV. 1 mSM = naQED(mZ) w 1 W sin2 flf 1 - Ar ’ mWM = 80.362-0031 GeV. mWrect = 80.379 ± 0.012 GeV, m)o,pect = 173.3 ± 0.4(exp) ± 0.5(theory) GeV. FCC-ee: The Lepton Collider 295 dominant unknown term of the perturbative expansion. As a consequence, the LEP and Tevatron measurements were able to infer the existence of a Higgs boson and to predict its mass within the SM: m|M = 98+21 GeV. (1.7) The LHC observed the production of the Higgs boson in 2012 for the first time, at a mass well compatible with this prediction in the context of the standard model and nothing else. The current overall situation of the standard model fit to the precision measurements available to date is summarised in Figure 1.4. The fit prediction for the W mass and the weak mixing angle [34] within the SM, namely mW = 80.3584 ± 0.0055mtop ± 0.0025mz ± 0.0018aQED ± 0.0020as ± 0.0001mH ± 0.0040theory GeV = 80.358 ± 0.008total GeV, sin2 <9ff = 0.231488 ± 0.000029mtop ± 0.000015mz ± 0.000035aQED ± 0.000010as ± 0.000001mH ± 0.000047theory = 0.23149 ± 0.00007total, (1.8) are also very compatible with the world average of their direct measurements within current uncertainties: mW = 80.379 ± 0.012 GeV, and sin2 <9ff = 0.23153 ± 0.00016. (1.9) 1.2.2 Opportunities at the Z pole Electroweakly-coupled new physics would appear either as additional/different con- tributions to the perturbative expansion of the electroweak observable predictions, similar to those shown in Figure 1.3, or as modifications of the tree-level couplings to leptons and quarks. From the agreement between the predictions and the direct measurements, it follows that the effect of new physics, if any, must be smaller than the current uncertainties. The next significant step in this quest is therefore to drastically reduce these uncertainties, typically by one order of magnitude or more. In this section, it is assumed that theoretical uncertainties can be brought, by the calculation of missing QED, EW and QCD higher orders within the standard model and nothing else, to a level similar to, or smaller than, that of the experimental uncertainties. This issue is addressed briefly in Section 1.5. Numerically, the FCC- ee is able to deliver about 105 times the luminosity that was produced by LEP at the Z pole, i.e. typically 1.5 x 1011 Z ^ p+p- or t+t- decays and 3 x 1012 hadronic Z decays. Measurements with a statistical uncertainty up to 300 times smaller than at LEP (from a few per mil to 10-5) are therefore at hand. Forward-backward and polarisation asymmetries at the Z pole are a powerful experimental tool to measure sin2 , which regulates the difference between the right-handed and left-handed fermion couplings to the Z. With unpolarised incoming beams, the amount of Z polarisation at production is a gL,e gR,e 2ve/ae . . 2 zieff /a Ae = —L-^---------}—y,, with ve/ae = 1 - 4sin 0W , (1.10) gL,e2 + gR,e2 1 + (Ve/ae)2 by definition of the effective weak mixing angle sin2 . The resulting forward- backward asymmetry at the Z pole amounts to Aj|B = 4AeAf. The experimental 296 The European Physical Journal Special Topics Fig. 1.4. From reference [35]: Contours of 68% and 95% confidence level obtained from fits of the standard model to the precision measurements available to date, in the (mtop,mw) plane. The grey area is the result of the fit without the direct measurements of the W, top, and Higgs masses, while the narrower blue area includes the Higgs boson mass measurement at the LHC. The horizontal and vertical green bands and the combined green area indicate the 1a regions of the mW and mtop measurements (world averages). control of the longitudinal polarisation of each of the beams can be made with the foreseen polarimeter (Sect. 2.7) with great accuracy. From the experimental point of view, the e+e- ^ Z ^ p+ p- process is a golden channel for an accurate measurement of AFb . The dominant source of experimental uncertainty arises from the knowledge of the centre-of-mass energy. Indeed, in the vicinity of the Z pole, AFB exhibits a strong ffs dependence (1.11) caused by the off-peak interference between the Z and the photon exchange in the process e+e- ^ p+p-. As suggested in Section 2.7, a continuous measurement with resonant depolarisation of non-colliding bunches should allow a reduction of this uncertainty to below 0.1 MeV. The resulting uncertainty on AFB amounts to 9 x 10-6 (a factor three larger than the statistical uncertainty), which propagates to an uncertainty on sin2 Off of 6 x 10-6. Among the other asymmetries to be mea- sured at the FCC-ee, the t polarisation asymmetry in the t^ nvT decay mode provides a similarly accurate determination of sin2 , with a considerably reduced a/s dependence. In addition, the scattering angle dependence of the t polarisation asymmetry provides an individual determination of both Ae and At , which allows, in combination with the AFB and the three leptonic partial width measurements, the vector and axial couplings of each lepton species to be determined. Similarly, heavy- quark forward-backward asymmetries (for b quarks, c quarks and, possibly s quarks) together with the corresponding Z decay partial widths and the precise knowledge of (s)^3dd w [i i 8nV2aqED(s) s - mZ FB 4 M _ m2GF (1 - 4sin2 Off)2 2s _ ’ FCC-ee: The Lepton Collider 297 Ae from the t polarisation, provide individual measurements of heavy-quark vector and axial couplings. An experimental precision better than 5 x 10-6 is therefore a robust target for the measurement of sin2 Off at the FCC-ee, corresponding to more than a thirty- fold improvement with respect to the current precision of 1.6 x 10-4 (Eq. (1.9)). Individual measurements of leptonic and heavy quark couplings are achievable, with a factor of several hundred improvement on statistical errors and, with the help of detectors providing better particle identification and vertexing, by up to two orders of magnitude on systematic uncertainties. For this accuracy to be instrumental in constraining new physics, the parametric uncertainties of the sin2 0ff SM prediction (Eq. (1.8)) need to be brought to a similar level. The largest parametric uncertainty on the prediction, 3.5 x 10-5, arises from the limited knowledge of the electromagnetic coupling constant evaluated at the Z mass scale. It is hoped that this figure can be reduced by a factor of two to three with a better determination of the hadronic vacuum polarisation, in part with future low-energy e+e- data and in part with the use of perturbative QCD [36]. The large luminosity offered by the FCC-ee allows a direct determination of «QED(m|) to be contemplated [37], from the slope of the muon forward-backward asymmetry as a function of the centre-of-mass energy in the vicinity of the Z pole (Eq. (1.11)). As displayed in Figure 1.5, the statistical uncertainty of this measurement is minimum just below (a/s = 87.9 GeV) and just above (a/s = 94.3 GeV) the Z pole. It is shown in reference [37] that the experimental precision on oqED can be improved by a factor 3-4 with 40 ab- at each of these two points. Because most systematic uncertainties are common to both points and almost perfectly cancel in the slope determination, the experimental uncertainty is statistics dominated as long as the centre-of-mass energy spread (90 MeV at the Z pole) can be determined to a relative accuracy better than 1%, which is deemed achievable at the FCC-ee every few minutes [38]. More studies are needed to understand if the oqED (m|) determination can profit from the centre-of-mass energy dependence of other asymmetries. An experimental relative accuracy of 3 x 10-5 on OQED(m|) can be achieved at the FCC-ee, from the measurement of the muon forward-backward asymmetry with 40 ab-1 of centre-of-mass energies ~3GeV below and ~3GeV above the Z pole. The corresponding parametric uncertainties on the sin2 Off and mW SM predictions are accordingly reduced from 3.5 x 10-5 and 1.8 MeV to 9 x 10-6 and 0.5 MeV, respectively. The next parametric uncertainty to address at the Z pole is that arising from the Z mass. The Z mass and width were determined at LEP from the line shape scan to be mZ = 91187.5 ± 2.1 MeV and rZ = 2495.2 ± 2.3 MeV, with data taken mostly at ffs = 89.4, 91.2, and 93 GeV. The statistical errors of 1.2 MeV and 2 MeV would be reduced below 5 keV and 8 keV at the FCC-ee, with data taken at 87.9, 91.2, and 93.9 GeV. In both cases, the systematic uncertainty was dom- inated at LEP by the error pertaining to the beam energy calibration (1.7 MeV, and 1.2 MeV). With a precision of 0.1 MeV on the centre-of-mass energy (Sect. 2.7) and the centre-of-mass energy spread [38] at the FCC-ee, the uncertainty on mZ improves accordingly. A similar improvement is expected for the Z width if the point-to-point relative accuracy on the integrated luminosity is reduced to 5 x 10-5 (Sect. 7). Overall experimental uncertainties of 0.1 MeV or better are achievable for the Z mass and width measurements at the FCC-ee. The corresponding parametric uncertainties on the sin2 Off and mW SM predictions are accordingly reduced to 6 x 10-7 and 0.12 MeV, respectively. The third and final parametric uncertainty to address at the Z pole comes from the knowledge of the strong coupling constant as(m|). The ratio R of the Z hadronic 298 The European Physical Journal Special Topics Fig. 1.5. Relative statistical accuracy of the gqed determination from the muon forward- backward asymmetry at the FCC-ee, as a function of the centre-of-mass energy. The inte- grated luminosity is assumed to be 40 ab-1 below and above the Z pole, and to follow the profile of Figure 1.2 for other centre-of-mass energies. The dashed blue line shows the current uncertainty. width to the Z leptonic width, = 20.767 ± 0.025, has been used, at LEP, for the determination of the strong coupling constant, which yielded as(m|) = 0.1196 ± 0.0028 (exp) ±0.0009 (theory). The experimental uncertainty was dominated by the statistics of the Z leptonic decays and therefore a combination of the three lepton species - with the assumption of lepton universality - was required. At the FCC- ee, the statistical uncertainty is negligible and the measurement of RM, yielding an experimental precision of 0.001 from the knowledge of the detector acceptance, suffices. The experimental uncertainty on as(m|) shrinks accordingly to 0.00015, as illustrated in Figure 1.6. A similar figure can be obtained from the measurements of the hadronic and leptonic decay branching ratio of the W boson [39], copiously produced with the FCC-ee running at larger centre-of-mass energies. An absolute (relative) uncertainty of 0.001 (5 x 10-5) on the ratio of the Z hadronic-to-leptonic partial widths (R^) is well within the reach of the FCC-ee. The same relative uncertainty is expected for the ratios of the Z leptonic widths, which allows a stringent test of lepton universality. The overall uncertainty on as(m|) obtained from R¿ drops by more than an order of magnitude. The corresponding parametric uncertainties on the SM predictions of sin2 and mW are accordingly reduced to 10-6 and 0.2 MeV, respectively. 1.2.3 Opportunities at the W+ W- and tt threshold The safest and most sensitive way to determine the W boson and top quark masses and widths is to measure the sharp increase of the e+ e- ^ W+W- and e+e- ^ tt cross sections at the production thresholds, at centre-of-mass energies around twice FCC-ee: The Lepton Collider 299 Fig. 1.6. Precision on as derived from the electroweak fit today (blue band from [35]) and expected at the FCC-ee (yellow band, without theoretical uncertainties and with the current theoretical uncertainties divided by a factor of four). All fits were performed with the GFitter software (http://cern.ch/gfitter/Software/index.html). the W and top masses (Fig. 1.7). In both cases, the mass can be best determined at a quasi-fixed point where the cross section dependence on the width vanishes: a/s ^ 162.5 GeV for mW and 342.5 GeV for mtop. The cross section sensitivity to the width is maximum at a/s ^ 157.5 GeV for rW, and 344 GeV for rtop. With 12 ab-1 equally shared between 157.5 and 162.5 GeV, a simultaneous fit of the W mass and width to the e+e- ^ W+W- cross-section measurements yields a precision of 0.5 MeV on mW and 1.2 MeV on rW. Lest the measurements be limited by systematic uncertainties, the following conditions need to be met. The centre- of-mass energies must be measured with a precision of 0.5 MeV. The point-to-point variation of the detector acceptance (including that of the luminometer) and the WW cross section prediction must be controlled within a few 10-4. Finally, the background must be known at the few per-mil level. These conditions are less strin- gent than the requirements at the Z pole - where the centre-of-mass energies must be measured to 0.1 MeV or better and the point-to-point variations of the luminometer acceptance must be controlled to 5 X 10-5, etc. In addition, the backgrounds can be controlled by an additional energy point below the W pair production threshold. An experimental precision of 0.5 (1.2) MeV for the W mass (width) is within reach at the FCC-ee, with 12 ab-1 accumulated at the W pair production threshold. The situation is slightly different for the top quark. A multipoint scan in a 4 GeV window will be needed for the top mass determination, because mtop might not be known to better than ±1 GeV from the theoretical interpretation of the hadron col- lider measurements. In addition, the tt cross section depends on the top Yukawa coupling, arising from the Higgs boson exchange at the tt vertex (Sect. 1.3.2). This dependence can be fitted away with supplementary data at centre-of-mass ener- gies slightly above the tt threshold. The non-tt background, on the other hand, 300 The European Physical Journal Special Topics Fig. 1.7. Production cross section of W boson (left) and top-quark pairs (right) in the vicinity of the production thresholds, with different values of the masses and widths. In the left panel, the pink and green bands include variations of the W mass and width by ±1 GeV. In the right panel, the grey and green bands include variations of the top-quark mass and width by ±0.2 and ±0.15 GeV. The dots with error bars indicate the result of a 10-point energy scan in steps of 1 GeV, with 0.02 ab-1 per point. needs to be evaluated from data at centre-of mass energies slightly below the tt threshold. With a luminosity of 25 fb-1 recorded at eight different centre-of-mass energies (340, 341, 341.5, 342, 343, 343.5, 344, and 345GeV), the top-quark mass and width can be determined with statistical precisions of ±17 MeV and ±45 MeV, respectively. The uncertainty on the mass improves to less than 10 MeV if the width is fixed to its SM value. Each of the centre-of-mass energies can be measured with a precision smaller than 10MeV from the final state reconstruction [40] of e+e- ^ W+W-, ZZ, and Zy events and from the knowledge of the W and Z masses, which causes a 3 MeV uncertainty on the top-quark mass. Today, the theory uncertainty due to missing higher orders in QCD is at the 40 MeV level for the mass and the width. An uncertainty of 17 (45) MeV is achievable for the top-quark mass (width) measurement at the FCC-ee, with 0.2 ab-1 accumulated around the tt threshold. The corresponding parametric uncertainties on the SM predictions of sin2 0W and mW are accordingly reduced to 6 x 10-7 and 0.11 MeV, respectively. It is only once all above measurements are performed that the total parametric uncertainty on the W mass and on sin2 0W predictions (0.6 MeV and 10-5, respec- tively), dominated by the in-situ precision on aqED(m|), can match the uncertainty on their direct determination (0.5MeV and 5 x 10-6, respectively). At the time of writing, the FCC-ee is the only future collider project that plans to realise this tour-de-force, a prerequisite for an optimal sensitivity to new physics beyond the standard model (Sect. 1.4.1). 1.2.4 Additional opportunities The measurement of the Z decay width into invisible states is of great interest as it constitutes a direct test of the unitarity of the neutrino mixing matrix - or of the existence of right-handed quasi-sterile neutrinos, as pointed out in reference [41]. At LEP, it was mostly measured at the Z pole from the peak hadronic cross section to FCC-ee: The Lepton Collider 301 be, when expressed in number of active neutrinos, Nv = 2.984±0.008. The measure- ment of the peak hadronic cross-section at the Z pole is dominated by systematic uncertainties, related, on one hand, to the theoretical prediction of the low-angle Bhabha-scattering cross section (used for the integrated luminosity determination), and to the absolute integrated luminosity experimental determination, on the other. At the FCC-ee, a realistic target for this systematics-limited uncertainty is bounded from below to 0.001, based on ongoing progress with the theoretical calculations and experimental technology. At larger centre-of-mass energies, the use of radiative return to the Z [42], e+ e- ^ Zy, is likely to offer a more accurate measurement of the number of neu- trinos. Indeed, this process provides a clean photon-tagged sample of on-shell Z bosons, with which the Z properties can be measured. From the WW threshold scan alone, the cross section of about 5 pb [43-46] ensures that fifty million Zy events are produced with a Z ^ vv decay and a high-energy photon in the detector acceptance. The 25 x 106 Zy events with leptonic decays, in turn, provide a direct measurement of the ratio r/ffrlff/ in which uncertainties associated with absolute luminosity and photon detection efficiency cancel. The 150 million Zy events with either hadronic or leptonic Z decays will also provide a cross check of the systematic uncertainties and backgrounds related to the QED predictions for the energy and angular distributions of the high energy photon. The invisible Z width will thus be measured with a dominant statistical error corresponding to 0.001 neutrino family. Data at higher energies contribute to further reduce this uncertainty by about 20%. A somewhat lower centre-of-mass energy, for example a/s = 125 GeV - with both a larger luminosity and a larger Zy cross section and potentially useful for Higgs boson studies (Sect. 1.3.2) - would be even more appropriate for this important measurement. The FCC-ee has the potential to deliver a measurement of the Z invisible width with an overall, statistics-dominated, uncertainty smaller than 0.0008 of a SM neu- trino partial width. A complete set of electroweak precision measurements also requires the pre- cise determination of the electroweak couplings of the top quark, which may carry enhanced sensitivity to new physics. It is shown in reference [47] that the polari- sation of the top quark arising from its parity-violating couplings to the Z in the process e+e- ^ tt allows a simultaneous measurement of these couplings without incoming beam polarisation, and with an optimal centre-of-mass energy of 365 GeV. With one million tt events (corresponding to an integrated luminosity of 1.5 ab-1 at a/s = 365 GeV), the vector and axial top-quark couplings to the Z can be measured with a precision of 0.5% and 1.5%, respectively, from an analysis of the angular and energy distributions of the leptons (e, p) coming from the top-quark semi-leptonic decays. The production cross section needs to be predicted with a couple of per-cent precision in order not to dominate the coupling uncertainties. A per-cent level precision can be reached on the vector and axial couplings of the top quark to the Z boson at the FCC-ee, with 1.5 ab-1 at ffs = 365 GeV. 1.2.5 Global electroweak Fit Once the W boson and the top-quark masses are measured with precisions of a few tenths and a few tens of MeV, respectively, and with the measurement of the Higgs boson mass at the LHC (to be further improved at the FCC-ee), the SM prediction of a number of observables sensitive to electroweak radiative corrections become absolute with no remaining additional parameters. Any deviation will be a demon- stration of the existence of new, weakly interacting particle(s). As just discussed, the FCC-ee offers the opportunity to measure such quantities with precisions between 302 The European Physical Journal Special Topics Fig. 1.8. Contours of 68% confidence level obtained as in Figure 1.4 from fits of the stan- dard model to the electroweak precision measurements offered by the FCC-ee, under the assumption that all relevant theory uncertainties can be reduced to match the experimen- tal uncertainties, in the (mtop, mW) plane. All fits were performed with the GFitter soft- ware (http://cern.ch/gfitter/Software/index.html). The red ellipse is obtained from the FCC-ee measurements at the Z pole, while the blue ellipses arise from the FCC-ee direct measurements of the W and top masses. One of the two blue ellipses is centred around the central values measured today, the other is central around the values predicted by the standard model (pink line) for mH = 125.09 GeV. The two dotted lines around the standard model prediction illustrate the uncertainty from the Z mass measurement if it were not improved at the FCC-ee. The green ellipse corresponds to the current W and top mass uncertainties from the Tevatron and the LHC, as in Figure 1.4. The potential future improvements from the LHC are illustrated by the black dashed ellipse. The cyan ellipse corresponds to the dark blue 68% CL contour of Figure 1.4 that includes all current Z pole measurements and the current Higgs boson mass measurement at the LHC. one and two orders of magnitude better than the present status. The theoretical pre- diction of these quantities with a matching precision is an incredible challenge, but the genuine ability of these tests of the completeness of the standard model to dis- cover new weakly-interacting particles beyond those already known is a fundamental motivation to take it up and bring it to a satisfactory conclusion. As an illustration, the SM can be fitted to all the electroweak precision observ- ables measured at the FCC-ee but the mW and mtop direct measurements. The result as obtained with the GFitter program [34], under the assumption that all relevant theory uncertainties can be reduced to match the experimental uncertain- ties, is displayed in Figure 1.8 as 68% CL contours in the (mtop,mW) plane. This fit is compared to the direct mW and mtop measurements at the W+W- and the tpt thresholds. A comparison with the precisions obtained with the current data at lepton and hadron colliders, as well as with LHC projections, is also shown. FCC-ee: The Lepton Collider 303 1.3 The Higgs boson Owing to its recent observation at the LHC, the Higgs boson is the least under- stood of all particles in the standard model. Accurate and model-independent measurements of its properties are in order to unravel its profile and to better understand the role it played/will play in the history of the universe. The LHC and its high-luminosity upgrade will provide insights into the Higgs boson couplings to the SM gauge bosons and to the heaviest SM fermions (t, b, t, p). A preci- sion that is qualitatively up to the 5% level will be achieved, under a number of model-dependent assumptions, in particular on the Higgs boson decays that cannot be accessed directly at hadron colliders. Interactions between the Higgs boson and other new particles at a higher energy scale A typically modify the Higgs boson cou- plings to SM particles (denoted gHXX for the coupling of the Higgs boson to particle X), either at tree level or via quantum corrections. Coupling deviations SgHXX/gHXX with respect to their SM predictions are in general smaller than 5% for A = 1 TeV, with a dependence that is inversely proportional to A2 . 1.3.1 Absolute coupling determination from the Higgs branching fractions From the previous argument, a sub-percent accuracy on a given coupling measure- ment would be needed to access the 10 TeV energy scale, and maybe to exceed it by an analysis of the deviation pattern among all couplings. Similarly, quantum correc- tions to Higgs couplings are at the level of a few % in the SM. The quantum nature of the Higgs boson can therefore only be tested if the measurement of its properties is pushed well below this level of precision, to a few per mil or better. An experimental sample of at least one million Higgs bosons has to be pro- duced and analysed to potentially reach this statistical precision. Production at e+ e- colliders proceeds mainly via the Higgsstrahlung process e+e- ^ HZ and WW fusion e+e- ^ (WW ^ H)vv. The cross sections are displayed in Figure 1.9 as a function of the centre-of-mass energy. The total cross section presents a max- imum at /s = 260 GeV, but the event rate per unit of time is largest at 240 GeV, as a consequence of the specific circular-collider luminosity profile. As the cross section amounts to 200 fb at this energy, the production of one million events requires an integrated luminosity of at least 5 ab-1 at /s = 240 GeV. This sam- ple, dominated by HZ events, is usefully complemented with 1.5 ab-1 luminosity collected at a/s = 365 GeV by about 180 000 HZ events and 45 000 WW-fusion events. At /s = 240 GeV, the determination of Higgs boson couplings follows the strat- egy described in references [8,48], with an improved analysis that exploits the supe- rior performance of the CLD detector design (Sect. 7). The total Higgs production cross section is determined from counting e+e- ^ HZ events tagged with a leptonic Z decay, Z ^ f+f-, independently of the Higgs boson decay. An example of such an event is displayed in Figure 1.10 (left). The mass mRecoil of the system recoiling against the lepton pair is calculated with precision from the lepton momenta and the total energy-momentum conservation: mRecoil = s + m| — 2/s(Ee+ + E¿- ), so that HZ events have mRecoil equal to the Higgs boson mass and can be easily counted from the accumulation around mH. Their number allows the HZ cross section, aHz, to be precisely determined in a model-independent fashion. This precision cross- section measurement alone is a powerful probe of the quantum nature of the Higgs boson. Under the assumption that the coupling structure is identical in form to the SM, this cross section is proportional to the square of the Higgs boson coupling to the Z, gHzz. Building upon this powerful measurement, the Higgs boson width can then be inferred by counting the number of HZ events in which the Higgs boson decays into a 304 The European Physical Journal Special Topics Fig. 1.9. The Higgs boson production cross section as a function of the centre-of-mass energy in unpolarised e+e- collisions. The blue and green curves stand for the Hig- gsstrahlung and WW fusion processes, respectively, and the red curve displays the total production cross section. The vertical dashed lines indicate the centre-of-mass energies of choice at the FCC-ee for the measurement of the Higgs boson properties. Fig. 1.10. Left: a schematic view, transverse to the detector axis, of an e+e — HZ event with Z—— ß+ß- and with the Higgs boson decaying hadronically. The two muons from the Z decay are indicated. Right: distribution of the mass recoiling against the muon pair, determined from the total energy-momentum conservation, with an integrated luminosity of 5 ab-1 and the CLD detector design. The peak around 125 GeV (in red) consists of HZ events. The rest of the distribution (in blue and pink) originates from ZZ and WW production. FCC-ee: The Lepton Collider 305 Table 1.1. Relative statistical uncertainty on = (¿Ą/)(Fi7+a0Fi), On = (I7m/) (Ir/) , (1.13) where / is the scalar doublet, / runs overall the 5 types of SM fermion multiplets, while F only refers to the 2 types of SM left-handed fermion doublets. A closer scrutiny of the operator O^D helps in gaining intuitive understanding of how these operators give rise to observable effects: when the Higgs vacuum expectation value is inserted into this operator, an additional contribution to the W/Z mass splitting is generated, beyond the usual SM prediction. Some of the above operators, as well as additional interactions absent in EWPO, enter Higgs boson observables, such as O0G = /t/ gAv+v, O0W = /W“ W“ +v, O0B = /t/sMv, O0n = (/t/)D(/t/), OM0 = (/t/)(/2/p), OT0 = (/t/)(/b/T ), (1.14) o60 = (/t/)(b3/6), OC0 = (/t/)(b2<^ c). For clarity and simplicity, the expected sensitivities to the above-mentioned dimension-six operators are estimated with a fit in which only one operator is present at a time. While these results are technically not model-independent, they still serve to illustrate the expected sensitivity improvement of future experimental data. The projected sensitivity to new physics obtained from the FCC-ee electroweak precision measurements is illustrated in Figure 1.12. These results assume that the intrinsic uncertainty of SM theory calculations will be reduced according to the conservative projections of reference [74]. The improvement of the SM parametric FCC-ee: The Lepton Collider 311 Fig. 1.13. Comparison of sensitivities from the SMEFT fit of the full FCC-ee set of EWPO, using the future SM theory uncertainties and those neglecting either the intrinsic errors, the parametric ones, or both. uncertainties due to the more precise measurements of the SM inputs at the FCC-ee is also taken into account, together with the expected advance in the determination of the strong coupling constant from lattice calculations. The sensitivities to the ratios Cj/A2 are reported as the 95% probability bounds on the interaction scale, A/ffCÎ, associated to each operator. This interaction scale must not be confused —1/2 with the mass scale of new particles, in the same way as the Fermi constant Gp ' does not represent the scale where new degrees of freedom, i.e. the W boson, enter in the electroweak theory. These bounds are compared to the results obtained from current electroweak precision data [75,76]. In general, an overall improvement of over one order of mag- nitude is expected in the sensitivity to Cj/A2. Not surprisingly, an even stronger constraining power could be achieved if theory uncertainties were further reduced, as shown in Figure 1.13. Figure 1.14 shows similar results for the case of a fit to the precise measure- ments of the Higgs boson observables. The corresponding limits on the interaction scale are compared to those from current LHC data [77]. The overall sensitivity to Cj/A2 can be, again, as large as ^20 times that of current data and up to 5-10 times that expected after the HL-LHC. The experimental uncertainties for the Higgs boson measurements are expected to be similar to or larger than those from SM calculations. More FCC-ee data would therefore allow the sensitivity to be improved even further, in some cases. Finally, Figure 1.15 compares both EWPO and Higgs boson constraints and shows also the resulting bounds obtained with the combination of both sets of observables. In these simplified fits to each inter- action individually, the EWPO and Higgs boson constraints are very much complementary. These fits must be used carefully when translated into specific scenarios, as they are not fully model-independent. The results, however, clearly demonstrate the important step that the FCC-ee physics programme represents with respect to any 312 The European Physical Journal Special Topics Fig. 1.14. FCC-ee Higgs constraints on the different EFT interactions in equa- tions (1.13) and (1.14), compared to the current LHC Run 2 results. The impact of the different types of SM theory uncertainties are also shown (neglecting intrinsic, parametric and both uncertainties, respectively). Fig. 1.15. Comparison of the separate EW and Higgs constraints, as well as the results combining both in a global SMEFT fit. Darker shades of each color indicate the results neglecting all SM theory uncertainties. FCC-ee: The Lepton Collider 313 existing experiments, in terms of the potential for comprehensive precision studies of the electroweak sector. 1.4.2 Sensitivity to new physics predicted in specific BSM models The fits presented in Section 1.4.1 are generic in that they make no specific assump- tion about the underlying BSM theory, except that its energy scale must be large with respect to the centre-of-mass energy. More specific extensions of the standard model have been proposed to explain the current agreement between observations at colliders and SM predictions, on the one hand, and the growing experimental evidence for new phenomena (non-baryonic dark matter, small neutrino masses, baryon asymmetry of the universe, ...), on the other. These extensions predict either very small deviations from standard model predictions in EWPO and Higgs precision measurements, or the existence of new light or heavy particles, or both, which could be tested at the FCC-ee. In particular, a multitude of Z decays that are predicted to be rare or forbidden in the SM can be studied or searched for in the 5 x 1012 events produced at the Z pole. In this section, the unique sensitivity of the FCC-ee to a selected but representative set of BSM models or situations is reviewed. Right-handed neutrinos Neutrino oscillations demonstrate that neutrinos have mass [78]. As such, they provide laboratory evidence for physics beyond the renormalisable interactions of the SM. Understanding the origin of neutrino masses would open the way to a deeper understanding of particle masses, as well as possible solutions to out- standing issues in particle physics such as the origin of the baryon asymmetry in the universe or of dark matter. A minimal and natural way to account for the observed smallness of neutrino masses is the existence of non-renormalisable Majo- rana neutrino mass terms, which can arise due to heavy right-handed neutrinos with Majorana mass terms [79-84]. For these reasons, in the discussion of future projects, experimental sensitivity to right-handed neutrinos (also named “sterile neutrinos”) has become one of the benchmarks for discovery potential. Right-handed neutrinos lead to a rich variety of signatures at the FCC-ee, from their impact on precision measurements to the possible observation of right-handed neutrino decays. It has been argued that in some scenarios the right-handed neutrino mass scale M can have a common origin with the electroweak scale [85-88]. The limit M ^ 0 gives rise to an approximate B — L symmetry, thus it is technically natural for M to be small. Reviews of how comparatively light right-handed neutrinos can address the fundamental puzzles of the baryon asymmetry of the universe and dark matter can be found in references [89-104]. Model classes that allow for a low scale see-saw are known as “inverse see-saw models” [79,80,105,106], and “linear see-saw models” [81,83,107-113], and are consistent with “minimal flavour violation” [84, 114]. A recent review of the collider phenomenology of neutrino mass models can be found in reference [115]. Right-handed neutrinos impact precision measurements through mixing with their left-handed counterparts, with angle O. After diagonalisation one has heavy and light mass eigenstates. The light neutrinos states, while remaining mostly left- handed, acquire a small sterile component yielding an apparent violation of the unitarity of the PMNS matrix [116]. The PMNS non-unitarity alters the couplings 314 The European Physical Journal Special Topics Fig. 1.16. Sensitivities of the different signatures to the active-sterile mixing angle 0 and sterile neutrino mass M at the FCC-ee, from reference [124]. In addition to the main signa- tures described in the text, the sensitivities from Higgs decays and mono-Higgs production is also shown. of the light neutrinos to the weak currents, thereby systematically shifting all the observables in which neutrinos are involved [117-123] and leading to a very specific pattern of deviations from the SM. The single most important observable is the Fermi constant Gp, which is mea- sured very precisely in muon decays p^ evMve, while being an input parame- ter for the electroweak precision observables. In the FCC-ee era, with many of these observables measured at the 10-5 precision level or better, a reduction of the neutrino coupling of that magnitude will be visible. Other observables that can be measured with great precision to test the PMNS matrix (non)unitarity include the charged current branching ratios, in particular t^ f v^ vT and W ^ f v¿), rare lepton-flavour-violating processes (f ^ f'y, f ^ 3f'), as well as weak cross sections for processes like e+e- ^ HZ, ZZ, and W+W-. For exam- ple, with 1.5 x 1011 tau lepton pairs produced, the tau leptonic branching ratios should be measurable to a relative precision of better than 10-5. Based on refer- ence [117], the sensitivity from the FCC-ee precision measurements in the plane (02,M) is shown by the horizontal blue lines in Figure 1.16. Two points should be noted. Firstly, the combination of lepton universality and the available EWPO will allow separate access to the three lepton flavour mixing angles. Secondly, the sensitivity to heavy neutrinos from precision measurements extends well beyond 100 TeV; this is a particular example of BSM physics for which decoupling is not at work. Heavy neutrinos N with masses M below mz and active-sterile mixing O below the present constraints [125] naturally have long lifetimes (~3 [cm]/|O|2(M [GeV])6), which can give rise to visible displaced secondary vertices in the detector, especially when the decay is semi-leptonic: N ^ fqq. Searches for heavy neutrino decays with detached vertices are most efficient during the Z pole run due to the larger luminosity and production cross section from Z ^ vN decays. These searches [126- 128] can reach sensitivities to active-sterile mixing parameters |O|2 down to and below ~10-11, as shown by the purple line in Figure 1.16, and by the orange line in the left panel of Figure 1.17. The search benefits from the suppression of the SM background due to the displaced vertex of the heavy neutrino decay. The small beam pipe radius and the clean experimental conditions are additional advantages. FCC-ee: The Lepton Collider 315 Fig. 1.17. Left: the region of sensitivity to the right-handed neutrinos as a function of their mixing angle 0 with active neutrinos and their mass M, in the displaced vertex search, put in perspective with the lower energy searches in neutrino beams or beam dump experiments (from Ref. [126], updated for the CDR FCC-ee conditions), and with theoretical constraints. Right: detail of the parameter space showing by colour code the number of events expected at the FCC-ee within the parameter space (thick black line) consistent with the leptogenesis hypothesis (from Ref. [129]); constraints from the DELPHI searches [125] and from neutrino oscillation data are shown. In both plots, normal mass ordering is assumed. The sensitivity could be improved to some extent by a larger tracking volume, but the dominant factor remains the huge luminosity at the Z pole. The right panel of Figure 1.17 indicates the number of events that would be observed as a function of M and |0|2. In some regions of the parameter space, several hundred signal events are expected to be observed, which would allow a first determination of the mass and lifetime of the right-handed neutrino and establish its relative decay rate into the three lepton flavours. This discovery, which would be made early in the life of the FCC-ee, would certainly have an impact on both detector design and motivation for FCC-hh, for which (i) dedicated displaced vertex triggers would be necessary; and (ii) the right-handed neutrinos would be produced most abundantly in W lep- tonic decays, thereby giving access to both initial and final state lepton charge and flavour. Hidden sector The evidence for the existence of dark matter is highly suggestive and has motivated innumerable searches for particle interactions of dark matter. The paucity of signals in searches for standard WIMP dark matter candidates, combined with an evolving theoretical perspective that increasingly takes inspiration from the visible sector features, has revealed that the nature of the dark sector could be much more complex than previously thought. The Higgs and Z-boson are unique as they are the only massive neutral bosons in the standard model. They are therefore prime candidates for probing the dark sector as they may decay readily to new light neutral fields beyond the SM. If these fields decay back into SM states, they could provide a unique window into the dark sector. Furthermore, a variety of evidence for physics beyond the SM points to new sectors that may have new light states. One popular class of models that offers an explanation for the insensitivity of the weak scale to new high energy physics scales in nature is known by the moniker of “neutral naturalness”. (The “Twin 316 The European Physical Journal Special Topics Higgs” [130] is the first incarnation of this idea.) This name originates from the fact that the particles that protect the Higgs boson mass from large quantum corrections are neutral. Furthermore, these models also often require, structurally, that some of the new particles are light and could thus show up in rare decays of the Higgs boson. Further motivation for the possibility of new neutral “hidden” sectors arises in many models of electroweak baryogenesis, in which the nature of the electroweak phase transition is modified to become strongly first order as the result of new neutral fields interacting with the Higgs boson. Due to the cleanliness of the detection environment and the large samples of Z and Higgs bosons available at the FCC-ee, non-standard decays, facilitated through the production of new hidden sector particles, could be probed down to very small branching ratios. In Figure 1.18 the results of two dedicated studies of exotic Z and Higgs-boson decays [131,132] are shown, where the decays occur through the production of new hidden sector particles. For both bosons, the reach in probing such hidden sectors at the FCC-ee would far surpass that attainable at the HL-LHC, with the constraints in both cases comparable to the rare decay constraints usually delivered in lower energy hadron physics at the intensity frontier. Composite Higgs models All the measurements in the Higgs sector so far are aligned with the SM predictions. Yet, it is not known whether at small distances the Higgs boson is a fundamental scalar field, or a composite bound state like all the other scalar particles observed thus far. Composite Higgs models are the particle physics version of the BCS theory of superconductivity. They also solve the hierarchy problem of the standard model owing to compositeness form factors taming the divergent growth of the Higgs boson mass upon quantum effects. Furthermore, the measured Higgs boson mass could well be consistent with the fact that such a (now composite) object arises as a pseudo Nambu-Goldstone Boson (pNGB) from a particular coset of a global symmetry breaking [133,134]. Models with a Higgs state as a pNGB generally also predict modifications of its couplings to both bosons and fermions of the SM, hence the measurement of these quantities, at either a hadronic or a leptonic collider, repre- sents a powerful way to test its possible non-fundamental nature [135]. In addition to deviations in the Higgs couplings, composite Higgs models also predict vector res- onances at a scale of a few TeV; heavy vector-like fermionic top partners that could mix with the top quarks and induce some sizeable deviations in the EW couplings of the top quark; and heavy vector-like top partners with exotic charges that could be searched for directly, for instance in same-sign di-lepton channels. The synergy and complementarity between these direct and indirect signatures have been discussed in the literature [136,137]. Concrete phenomenological studies for FCC-ee have been carried out considering an explicit four-dimensional model which realises this idea of Higgs compositeness (4DCHM) [138]. This model features new neutral massive gauge bosons, hereafter denoted by Z2 3, with mass larger than ~3TeV that could escape detection at the LHC owing to the small Zi couplings to both light quarks and leptons [139], combined with possibly very large widths of the Zi states. Such additional EW gauge bosons would however enter the e+e- ^ tt cross Section [140], in a twofold way. On the one hand, their presence can be felt through mixing effects with the Z state of the SM that would modify the Ztt and the Zf+f- couplings. On the other hand, new Feynman diagram topologies with the propagation of such Z2 3 states would also enter top-pair production and appear as effective ytt coupling modifications. The FCC-ee: The Lepton Collider 317 Fig. 1.18. Expected upper limits on the branching ratios for the exotic decays of the Higgs boson (top) and Z boson (bottom) that can be accessed at FCC-ee, including decays involving dark matter. These figures are taken from [131,132]. The large and experimentally clean samples of these bosons allow for the discovery of exotic decays even for very small exotic branching ratios. For exotic Z decays expected limits for the worst- and best-case scenario are shown. modification of the Zf+f- couplings would also affect other processes, specifically e+ e- ^ p+ p-. To evaluate the sensitivity of the FCC-ee to these models, a benchmark point A was identified to evade the latest projected bounds of the HL-LHC searches for Z! gauge bosons and to be compatible with current EWPO measurements, by the following choice of 4DCHM gauge sector parameters: the compositeness scale f is set to 1.6 TeV, and the strong gauge coupling g* to 1.8 [138]. With these parameters, the Z! masses amount to mz/ = 2.98 TeV and mz/ = 3.07 TeV, and their widths are all of the order of 20-30% of their masses. As shown in Figure 1.19, the large statistics offered by the FCC-ee would reveal significant deviations in almost all observables mentioned above with respect to the SM: top-quark left and right couplings to the Z (4a), effective top couplings to the photons (8a), Higgs boson couplings to the Z boson and to the b quark (13a), or e+e- ^ p+p- cross sections above the Z pole (>20a). With such a pattern of significance, these measurements in principle allow the model parameters to be accurately fit. For example, the Z' masses would be predicted with a precision of 50 GeV (2%), the scale f with a precision of 130 GeV 318 The European Physical Journal Special Topics Fig. 1.19. Predicted deviations of the top-quark left and right couplings to the Z (top left) and effective couplings to the photon (top right), of the Higgs boson couplings to the Z boson and the b quark (bottom left), and of the dimuon cross section as a function of the centre-of-mass energy (bottom right) for the 4DCHM benchmark point A (represented by a cyan marker in the first three graphs) with respect to the SM, centred at (0,0) in the first three graphs, and at 0 in the fourth. The FCC-ee measurement uncertainties are displayed either as red ellipses or as error bars. The black markers in the top-left and bottom-left plots show the deviations predicted by other 4DCHM parameter sets, with f < 1.6 TeV. (8%), and the coupling constant g* with a precision of 0.14 (8%) with the sole p+ p observables. Lepton flavour violating Z decays The observation of flavour-violating Z decays, e.g. Z ^ ep, pT, or eT, would provide indisputable evidence for physics beyond the SM. These decays are forbidden in the SM by the GIM mechanism [141] and their branching fractions are still predicted to be extremely small (below 10-50) when the SM is minimally extended to incorporate flavour violation in the neutral lepton sector (LFV) induced by the leptonic mass mixing matrix [142]. Sizeable rates for these LFV Z^ processes could, hence, reflect the existence of new particles such as right-handed neutrinos. The search for LFV Z decays is also complementary to the direct search for heavy neutral leptons. A phenomenological study [143] addresses the potential for the FCC-ee to probe the existence of sterile neutral fermions in the light of the improved determination of neutrino oscillations parameters, the new bounds on low-energy LFV observables, as well as cosmological bounds. This work also addresses the complementarity of these searches with the current and foreseeable precision of similar searches at lower energy experiments. The best sensitivity to observe or constrain LFV in the ep sector is then obtained by the experiments based on the muon-electron conversion FCC-ee: The Lepton Collider 319 in nuclei [144]. In contrast, the study of the decays Z ^ eT and Z ^ pT provides an invaluable and unique insight into the connection to the third generation. The current limits on the branching ratios of charged lepton flavour violating Z decays were established by the LEP experiments [145-147]. More recently, the ATLAS experiment improved the bound for ep final states [148]. Typical upper limits on the branching fractions are at the level of 10-5 —10-6. The production at FCC-ee of 5 x 1012 Z decays provides improved limits by several orders of magnitude and probes BSM physics scenarios for branching fractions down to 10-9 [149]. Electroweak Penguins in b-quark transitions The production of all species of heavy flavours in a sample of 1012 Z ^ bb events, with a large boost as in the LHCb experiment, makes the FCC-ee a natural home for precision flavour physics. Processes involving a quark transition b ^ sf+f- (f denotes here an electron or a muon) are currently receiving substantial phenomeno- logical [150-153] and experimental [154-156] interest. The departures from the SM predictions observed in these studies question, in particular, the lepton uni- versality in quark-based transitions and may even suggest BSM physics with new gauge bosons or leptoquarks. Should these deviations be confirmed, observables involving the third generation charged lepton t may enhance the evidence and shed new light on the new physics involved. In this respect, the Bs ^ t + t- and B0 ^ K*°(892) t+T- decays are obvious candidates to study. The presence of neu- trinos in the final states makes the experimental reconstruction of these decays particularly challenging at hadron colliders. At the FCC-ee, however, the excellent knowledge of the decay vertices of multi-hadronic t decays allows the kinematics of these decays to be fully and unambiguously reconstructed. Identification of the dif- ferent hadron species in the tracking system of the detector would be an additional advantage to further reduce the background. About 1000 events with a reconstructed B0 ^ K* (892) t +t- decay are expected at the FCC-ee, which opens the way to measuring the angular properties of the decay [157] and, therefore, to a much refined characterisation of the potentially underlying new physics. Figure 1.20 displays the reconstructed B0 mass distribution of simulated SM signal and background events in a sample of 5 x 1012 Z decays in the CLD detector design. The signal purity and yield obtained at the FCC-ee are unequalled at any current or foreseeable collider and would increase in a corre- lated manner with any improvement to the charge-particle track impact parameter resolution. Other unique opportunities in flavour physics The study of the two rare decays above has shown that the statistics available at a high-luminosity Z factory, complemented by state-of-the-art detector performance, can allow their potential measurement at unequalled precision. They can also serve as a benchmark to open the way to other physics observables in quark and lepton sectors. The loop-induced leptonic decays Bd,s ^ e+e-, p+p-, and t + t- provide SM candles and are sensitive to several realisations of BSM physics. The obser- vation of Bs ^ t+T- would be invaluable in this respect and, with 100 000 events expected, is reachable at the FCC-ee. The charged-current-mediated leptonic decays Bu,c ^ pvp or tvt offer the possibility to determine the CKM elements |VUb| |Vcb| with mild theoretical uncertainties. The CP violation in mixing can be measured through semileptonic asymmetries, as yet unobserved, but the FCC-ee sensitivity is 320 The European Physical Journal Special Topics Fig. 1.20. Invariant mass of B0 ^ K*°(892) t+t reconstructed candidates (dots with error bars). In the selected events, the t particles decay into three prongs t- ^ vt allowing the t decay tertiary vertex to be reconstructed. The primary vertex (Z vertex) is reconstructed from primary charged particle tracks, and the secondary vertex (B0 vertex) is reconstructed with the K*(892) daughter particles (K*(892) ^ K+ n-). The dominant sources of backgrounds included in the analysed sample, namely Bs ^ D+D-K*°(892) and B0 ^ D+K* (892) t-Vt, are modelled by the red and pink probability density functions (p.d.f.), respectively. The signal p.d.f. is displayed with the green curve. close to their SM predictions. The cleanliness of the e+e- experimental environment will benefit the study of Bs, Bc and b baryons, the decay modes involving neutral particles in the final state (no, KS, n, n^v), as well as the many-body fully hadronic b-hadron decays. The harvest of CP-eigenstates in several b-hadron decays will allow the CP-violating weak phases to be comprehensively measured. 1.5 Requirements 1.5.1 Collider In 2013, the European Strategy for Particle Physics (ESPP) unambiguously recog- nised the importance of an electron-positron collider able to measure the properties of the Higgs boson and other particles with an unprecedented accuracy. In order to significantly increase the sensitivity to new physics of these measurements, such an e+ e- factory must deliver integrated luminosities at centre-of-mass energies from around the Z pole to above the tt threshold such that the statistical precision of most electroweak and Higgs observable measurements improves by one to two orders of magnitude. The minimum data samples needed to achieve this ambitious goal correspond to: 1. An integrated luminosity of at least 30 ab-1 at /s ^ 88 and 94 GeV for the measurement of the electromagnetic coupling constant at the Z mass scale. These data are also useful for the determination of the Z decay width. 2. An integrated luminosity of at least 100 ab-1 at /s ^ mz ^ 91.2 GeV in partic- ular, for the measurement of the effective weak mixing angle and for the search for, or study of, rare decays. These data are also important for the determination of the Z mass and of the strong coupling constant at the Z mass scale. FCC-ee: The Lepton Collider 321 3. An integrated luminosity of at least 10 ab-1 around the W+W- production threshold, for the measurement of the W mass and decay width, evenly shared between y/s ~ 157.5 and 162.5 GeV. These data are also important for the deter- mination of the number of neutrino species and an independent measurement of the strong coupling constant. 4. An integrated luminosity of at least 5 ab-1 at = 240 GeV, for the measure- ments of the Higgs boson couplings from its decays branching fraction and the total HZ production cross section. 5. An integrated luminosity of about 0.2 ab-1 in a 5-GeV-wide window around the tt threshold, typically shared among eight centre-of-mass energy points from ^340 to ^345 GeV, for the measurement of the top-quark mass, decay width, and Yukawa coupling to the Higgs boson. 6. An integrated luminosity of at least 1.5 ab-1 above the tt threshold, y ~ 365 GeV, for the measurement of the top electroweak couplings. These data also provide a threefold improvement of the Higgs boson decay width accuracy with respect to the sole data at y = 240 GeV, which in turn, significantly constrains the Higgs boson couplings. Over the whole period, the collider design must be compatible with operating at the Z pole every now and then to accumulate a few 107 Z decays in less than a day, for detector calibration purposes. (This important feature, used repeatedly during the second phase of LEP, cannot be proposed with current linear collider designs.) The unprecedented precision measurements achievable with these data in the electroweak, Higgs and top sectors are complementary and altogether sensitive to new physics scales up to 70 TeV. The Z factory run with 5 x 1012 Z can discover dark- matter candidate particles which couple with a strength down to as little as 10-11 of the weak coupling. Furthermore, with the synergetic runs at 240 and 365 GeV in combination with HL-LHC, the top Yukawa coupling will be known with a precision at the ±3% level, and the trilinear Higgs self coupling to ±34%. At this stage of the study, it appears that once the desired luminosity is accu- mulated at each of these energies, the potential gain in the precision of the Higgs boson and other particle properties is not enough (if any) to justify an upgrade to larger centre-of-mass energies, e.g. y = 500 GeV, especially with the perspective of a 100 TeV proton-proton collider operating later in the same tunnel. (Of course, the appearance at the LHC of some threshold for new physics accessible in e+e- colli- sions above 365 GeV may change the picture entirely.) On the other hand, many of the measurements offered by the FCC-ee between the Z pole and a maximum energy of 365 GeV, above the tt threshold, would still be limited by statistical uncertainties and would continue to improve with higher luminosity. It can be argued that experiments might wish to study the Higgs boson as a priority, rather than devoting the first six years at the Z pole and the WW threshold. There is indeed no fundamental obstacle to run first at y = 240 GeV, should it be felt compelling by the community. From the point-of-view of the machine installation and evolution, however, the proposed staging plan results from the most natural, efficient, economic, and logical operation model. From the scientific point-of-view, changing the order of the energy points would not change the overall outcome of the programme. Also, the perceived urgency of the Higgs precision measurements might well be not as incisive after 15 years of measurements at the LHC and the HL-LHC as it is today. Moreover, the EFT analysis reveals that the EW precision measurements at the FCC-ee have sensitivity to heavy new physics that is higher than, albeit complementary to, the Higgs precision measurements, and therefore offers no decisive arguments in favour of a different operation model. 322 The European Physical Journal Special Topics While the twofold symmetry of the current tunnel design (arguably tailored for the FCC-hh) limits the number of e+e- interaction points to two, a fourfold symmetry would open the possibility to profit from four interaction points (as was checked for LEP3 in the LEP tunnel) and therefore roughly double the total inte- grated luminosity collected in a given amount of time. A striking illustration is that of the trilinear Higgs self coupling [158]. With four IPs, two years at the Z pole and one year at the WW threshold would suffice to get the same integrated luminosity as after six years with two IPs (with the additional benefit of an earlier start of the Higgs precision measurement phase). The saved years and the four detectors could be optimally used to accumulate about 12 ab-1 at 240 GeV and 5.5 ab-1 at 365 GeV. The larger data sample would yield a measurement of the Higgs self coupling with a precision of ±25%, reduced to ±21% in combination with the HL-LHC, and to ±9% if only the Higgs self-coupling is allowed to vary. The first 5a demonstration of the existence - or, equivalently, the discovery - of this coupling is therefore within reach at the FCC-ee. The already strong scientific case of the FCC-ee is much stronger with four IPs instead of two. While the rest of this study is conservatively presented with two IPs only, more work will be devoted in the near future to investigate this interesting configuration. A feature unique to circular e+e- colliders is the possibility to use transverse polarisation of the incoming beams as a tool for precision beam energy calibration. A precision of the order of 100 keV on the centre-of-mass energy is a high-priority target at the Z pole and at the W pair threshold, for absolute measurements of the Z and W masses with the promised accuracies. Measurements of the beam energy and of the beam energy spread are also compulsory for the determination of most EWPOs, which show a strong dependence on these two quantities. On the other hand, the study demonstrated that longitudinal polarisation of the incoming beams provides no information that cannot be obtained otherwise with the large FCC-ee luminosity. Electroweak observables accessible with longitudinal polarisation can be measured with a similar accuracy from either unpolarised asymmetries [159] or by using the measurable polarisation of weakly decaying final state particles such as the top quark [47] and the t lepton. Finally, a unique possibility of the FCC-ee is operate at ffs — mH — 125 GeV, with moderate centre-of-mass energy monochromatisation. The study showed that, for such a mode of operation, a data sample corresponding to an integrated luminos- ity of at least 10 ab-1 would be a valuable addition to constrain the Yukawa coupling of the electron to the Higgs boson. These data would also allow the precision of the number of neutrino species to be improved by a factor two with respect to the same amount of data at the W pair threshold. 1.5.2 Detectors As mentioned above, circular colliders have the advantage of delivering collisions to multiple interaction points, which allow different detector designs to be studied and optimised. On the one hand, the planned performance of heavy-flavour tagging, of particle identification, of tracking and particle-flow reconstruction, and of lepton, jet, missing energy and angular resolution, need to match the physics programme and the statistical precision offered by the FCC-ee. On the other hand, the detectors must satisfy the constraints imposed by machine performance and interaction region layout: the occupancy from beam-induced background needs to be minimised; the interaction rates (up to 100 kHz at the Z pole) put strict constraints on the event size and readout speed; due to the beam crossing angle, the detector solenoid mag- netic field is limited to 2 T to confine its impact on the luminosity; the accurate FCC-ee: The Lepton Collider 323 measurement of the significant centre-of-mass energy spread (90 MeV at the Z pole, 500 MeV at the highest FCC-ee energies) requires an angular resolution better than 100 prad for muons; the luminometer must be situated only 1 m away from the interaction point, but still provide a precision better than 10-4 on the luminosity; etc. Two detector concepts have been studied and optimised for the FCC-ee, and are briefly presented in Section 7: (i) CLD, a consolidated option based on the detector design developed for CLIC, with a silicon tracker and a 3D-imaging highly-granular calorimeter; and (ii) IDEA, a bolder, possibly more cost-effective, design, with a short-drift wire chamber and a dual-readout calorimeter. It was demonstrated that detectors satisfying the requirements are feasible. The particular choice of detectors, motivated by the wish to explore the technol- ogy and cost spectrum, is of course not unique. The optimisation of these two con- cepts must continue, but other concepts might actually prove to be better adapted to the FCC-ee physics programme and need to be studied in the near future in order to move towards timely FCC-ee detector proposals. At the same time, a more concrete study of systematic uncertainties must be done to match the statistical precision available. 1.5.3 Theory The opportunities offered by the FCC-ee luminosities at centre-of-mass energies ranging from around the Z pole to above the tt threshold allow improvements of between one and two orders of magnitude on the experimental accuracy of most elec- troweak and Higgs precision observable measurements, with respect to the achieve- ments of previous e+e- and hadron colliders. To fully capitalise upon these high precision measurements by testing the pre- dictions of the Standard Model, it is necessary that theoretical uncertainties will be subdominant to experimental uncertainties. A dedicated study of the future of precision SM calculations has been undertaken [160]. A group consisting of nearly 30 theoreticians interested in the project has been formed for this purpose. A first proposal for training and study with precision calculations is included in the R&D part of this report (Appendix A). It comprises a five-year initial plan, but further continuation is being discussed. The results of [160] are summarised as follows. At the electroweak scale it is estimated that for the precision electroweak pseudo- observables mw, sin2 $W, rz, Rb, and Rq projected intrinsic errors arising due to uncalculated higher order perturbative corrections will be comparable to experi- mental errors at the time of FCC-ee running. The same is true for the parametric errors arising due to uncertainties in the SM input parameters. For the Higgs factory operation, all relevant intrinsic errors can be reduced to less than the anticipated experimental sensitivity. Parametric errors are expected to be subdominant when compared to experimental errors. The exception is the case of Higgs boson decays to charm and bottom quarks, where the parametric errors due to the quark-mass uncertainty in the inputs can still be at the same level as the expected experimental precision. The complexity of the task ahead in minimising theoretical errors is similar to that of the computations required for the HL-LHC data and the necessary tools have been identified [161]. These studies demand focussed investment and support by the community in order to reach the necessary level of development. With this investment, it is estimated that all main obstacles can be overcome in the course of the preparations, before the actual operation of the accelerator. 324 The European Physical Journal Special Topics 2 Collider design and performance 2.1 Requirements and design considerations The FCC-ee lepton collider is designed to provide e+e- collisions with centre-of- mass energies from 88 to 365 GeV. The centre-of-mass operating points with most physics interest are around 91 GeV (Z pole), 160GeV (W± pair-production thresh- old), 240GeV (ZH production) and 340-365GeV (tt threshold and above). The machine should accommodate at least two experiments operated simultaneously and deliver peak luminosities above 1 x 1034 cm-2 s-1 per experiment at the tt threshold and the highest ever luminosities at lower energies. The layout of the FCC-ee collider follows the layout of the FCC-hh hadron collider infrastructure, which has been developed with a view to its integration with the existing CERN accelerator complex as injector facility. As is the case for the hadron collider, beam with adequate quality can be provided by an upgrade of the existing injector complex. Alternatively, a dedicated optimised injector could be built. Care has been taken to ensure easy implementation of transfer lines from the SPS to the future collider tunnel. 2.2 Layout and key parameters 2.2.1 Layout The design goal is to maximise the luminosity for each energy under the following constraints: - Apart from ±1.2 km around each interaction point (IP), the machine should follow the layout of the 97.75 km circumference hadron collider [9]. - There should be two interaction points, located in the straight sections at PA and PG as shown in Figure 2.1. - Synchrotron radiation power should be limited to 50MW/beam at all energies. Figure 2.1 shows the layout of the FCC-ee together with FCC-hh. For FCC-ee, the design principles are - A double ring collider. - A horizontal crossing angle of 30mrad at the IP, with the crab waist collision scheme [11,12]. - The critical energy of the synchrotron radiation of the incoming beams towards the IP is kept below 100 keV at all beam energies. - A common lattice for all energies, except for a small rearrangement in the RF section for the tt mode. The betatron tune, phase advance in the arc cell, final focus optics and the configuration of the sextupoles are set to the optimum at each energy by changing the strengths of the magnets. - The length of the free area around the IP (f*) and the strength of the detector solenoid are kept constant at 2.2 m and 2 T, respectively, for all energies. - A “tapering” scheme, which scales the strengths of all magnets, apart from the solenoids, according to the local beam energy, taking into account the energy loss due to synchrotron radiation. - Two RF sections per ring placed in the straight sections at PD and PJ. The RF cavities will be common to e+ and e- in the case of tt. - A top-up injection scheme to maintain the stored beam current and the luminosity at the highest level throughout the physics run. It is therefore necessary to have a booster synchrotron in the collider tunnel. The integrated luminosity will be FCC-ee: The Lepton Collider 325 Fig. 2.1. The layouts of FCC-hh (left), FCC-ee (right), and a zoomed view of the trajectories across interaction point PG (right middle). The FCC-ee rings are placed 1m outside the FCC-hh footprint in the arc. In the arc the e+ and e- rings are horizontally separated by 30 cm. The main booster follows the footprint of the hadron collider. The interaction points are shifted by 10.6 m towards the outside of FCC-hh layout. The beams coming toward the interaction points are straighter than the outgoing ones in order to reduce the synchrotron radiation at the IP. reduced by more than an order without the top-up, due to ramping (~1/2), reduction of the beam-beam parameter 1/2 — 1/4), lower beam current (~1/2) at a lower injection energy, loss of stability of the machine (~1/2), etc. The FCC-ee inherits two important aspects from the previous generations of e+ e- circular colliders. At and above the tt threshold, the FCC-ee will encounter strong synchrotron radiation with the associated rapid damping. This situation is reminiscent of earlier high-energy colliders, especially LEP2. By contrast, at the Z pole, FCC-ee will operate with much less damping, but with a high beam current and a large number of bunches. This mode of operation mode was successfully established by several high-intensity colliders, such as the two B factories and DA$NE. There are two reasons for choosing a double-ring collider. Firstly, at low energies, especially at Z, more than 16 000 bunches must be stored to achieve the desired luminosity. This is only possible by avoiding parasitic collisions with a double-ring collider. Secondly, at the highest energy tt, although the optimum number of bunches reduces to ^30, the double ring scheme is still necessary to allow “tapering” [162]. The local energy of the beam deviates by up to ±1.2% between the entrance and the exit of the RF sections, with the result that the orbit deviation due to the horizontal dispersion in the arc and the associated optical distortion becomes intolerable. The optics may even fall into an unstable region. The tapering scheme restores the ideal orbit and optics almost completely. In the case of a single ring, the tapering scheme cannot be applied to the e+e- beams simultaneously. The number of IPs is restricted by the current layout choice for the straight sections in the FCC-hh. The straight sections around PD and PJ do not have large caverns for detectors. The intermediate straight sections at PB, PF, PH and PL are placed asymmetrically in the arcs and are not a suitable location for the FCC-ee RF cavities. Therefore, with this twofold ring symmetry, two IPs are the only solution for the FCC-ee. (It has, however, been demonstrated that four IPs would be possible for a ring of four-fold symmetry.) The resulting beam optics [162] have a complete 326 The European Physical Journal Special Topics periodicity of two. The beam lines for e+ and e- have a mirror symmetry with respect to the line connecting the two IPs and the beam optics are identical. The crab waist scheme [11,163,164] is essential to boost the luminosity by more than four orders of magnitude at Z, compared to previous colliders. This scheme gives a very small beam size at the IP together with a large crossing angle and small emittances, without exciting harmful synchrotron-betatron resonances associated with the crossing angle [164]. This scheme simply needs a pair of static sextupole magnets at both sides of the IP. These sextupoles are incorporated in the local chromatic correction system (LCCS) [162]. The effect of the crab waist is produced by reducing the strengths of some sextupoles in the LCCS, so there is no need for special hardware. The optimum parameters with the crab waist scheme including ß*s, bunch intensity, bunch length, etc., are obtained by the procedures described in the next section. The optimisation takes into account beamstrahlung - synchrotron radiation caused by the coherent EM field of the opposite bunch [164-168] - and various other beam-beam effects. The layout around the IP including the crossing angle, the strengths of solenoids and beam pipes are common for all energies. The polarity as well as the strengths of final quadrupoles change according to the beam energy and optimum focusing. 2.2.2 Beam parameter optimisation One of the main factors determining collider performance is the beam-beam inter- action, which at high energies can gain an extra dimension due to beamstrahlung. FCC-ee will be the first collider where beamstrahlung plays a significant role in the beam dynamics. Only half of the ring with one IP will be discussed in this section, because the other half will behave in the same way due to symmetry. To avoid confusion, the half-ring tunes will be marked by the superscript*. The luminosity per IP for flat beams (ax ^ ay) can be written as: (2.1) where /tot is the total beam current which is in this case determined by the synchrotron radiation power limit of 50 MW per beam. Therefore L can only be increased by making the vertical beam-beam parameter *y larger and ß* smaller while keeping the hour-glass factor RHG reasonably large. The latter depends only on Lj/ß* ratio, where Lj is the length of interaction area which in turn depends on the bunch length az and Piwinski angle ß: (2.2) (2.3) here 0 is the full crossing angle, see Figure 2.2. The beam-beam parameters for 0 = 0 become [169]: (2.4a) (2.4b) T 7 1tot £> L — • - • Rhg, 2ere ß* HG’ ß=utan ( 2 ) ' J az N 2ax L L j — . ^ , y + ß2 0»1, e<1 o * = Npre ß* Npre 2ß* x 2n7 (1 + ß2) <=» 1, e<= 1 n7 (az0)2 ’ * = Npre ^ ßy Npre ^ /ß* y 2n7 axay y + ß2 0»1, ö«1 ^7 az^ £s ’ FCC-ee: The Lepton Collider 327 Fig. 2.2. Sketch of collisions with a large Piwinski angle. where Np is the number of particles per bunch. Note that £X « 1/eX (in head-on collision) transforms to £X « ßX/a:? when ß ^ 1, and dependence on aX vanishes. In the following, the main parameters that need to be optimised are listed: - The vertical emittance should be as small as possible, but there are two restric- tions: e* > 0.002 • eX and e* > 1 pm. - At Z there is some contribution to e* (0.2-0.3pm) coming from the detector solenoids. It follows that eX should also be minimised, but there is no gain by reducing it below 0.4 nm. - An important parameter for the luminosity is ß*, whose minimum value is 0.8 mm and which is limited by the dynamic aperture. - It is assumed that can be easily controlled by Np, which implies that the number of bunches is adjusted to keep /tot unchanged. - Finally, it should be noted that ß*, the RF voltage (which determines the bunch length and the synchrotron tune), and the betatron tunes are relatively free parameters. Optimisation at the Z pole Since the FCC-ee is designed for a wide range of beam energies, parameter optimi- sation looks different at various energies. To find the good working points at the lowest energies (44-47 GeV), a scan of betatron tunes was performed in a simplified model: linear lattice, and weak-strong beam-beam simulations (without coherent instabilities). The results are presented in Figure 2.3. Since £X ^ , the footprint looks like a narrow vertical strip, with the bottom edge resting on the working point. Particles with small vertical betatron amplitudes have maximum tune shifts and are in the upper part of the footprint, so that the strong resonances of Figure 2.3, such as QX + 2Q* = n, come closer. Thus the good region is reduced to the red triangular area bounded by the main coupling resonance QX — Q* = n, sextupole resonance QX + 2Q* = n, and half-integer resonance 2QX = 1 with its synchrotron satellites. All other higher-order coupling resonances are suppressed by the crab waist and, therefore, not visible. As seen from the plot, the range of permissible QX for large is bounded on the right by 0.57-0.58. At the Z pole and the WW threshold, the main problems associated with the beam-beam interaction come from the two new phenomena found in beam- beam simulations: coherent synchrotron-betatron (x—z) instability [170-172] and 3D flip-flop [172], the latter occurring only in the presence of beamstrahlung. Both instabilities are bound with the horizontal synchro-betatron resonances, satellites of half-integer. In any case, it is necessary to move away from low-order resonances, so QX is chosen close to the upper limit (thus QX,* move further away from the integer, which facilitates tuning of linear optics). Another requirement is that £X must be substantially less than the distance between neighbouring satellites, which is equal to the synchrotron tune Q*. In other words, it is necessary to reduce the ratio Cx/Q* . 328 The European Physical Journal Special Topics Fig. 2.3. Luminosity at Z as a function of betatron tunes. The colour scale from zero (blue) to 2.3 x 1036 cm-2 s-1 (red). The white narrow rectangle above (0.57, 0.61) shows the footprint due to the beam-beam interaction. A few synchrotron-betatron resonance lines QX — rnQ*s = n/2 are seen. The first step is to reduce ß*. However, because of the absence of local horizontal chromaticity correction in the interaction region, attempts to make ß* too small lead to a decrease in the energy acceptance. ß* can be reduced to 15 cm at Z, but this is not enough to suppress the instabilities. The next step is to reduce for a given ß*, whilst trying to keep unchanged. This can only be done by increasing az. The most efficient way is to increase the momentum compaction factor ap, because not only does decrease (due to larger az) but also Q* grows. In addition, larger raises the threshold of microwave instability to an acceptable level. The only drawback of this approach is that the horizontal emittance eæ grows with the power of 3/2 with respect to ap. For the luminosity, eæ is not so important by itself, but ey should be small and it is normally proportional to eæ. However, the horizontal emittance at Z with small and FODO arc cells with 90°/90° phase advances is small - less than 90 pm. Therefore, even a threefold increase still allows achieving the design vertical emittance ey = 1 pm. Thus, the FCC-ee features a lattice where doubling of is achieved by reducing the phase advance per FODO cell in the arcs to 60°/60°, see Section 2.4.1. Turning to the dependence on RF voltage: az « 1/%/Vrf, Q* « VVrF. The requirement to keep unchanged means that Np/az is held constant. Therefore, if FCC-ee: The Lepton Collider 329 Vrf is lowered, £X decreases inversely with az (and not with the square of the inverse bunch length, as it might have seemed at first glance). As a result, £X/Q* does not change, but by lowering Q* the order of synchro-betatron resonances located in the vicinity of working point is increased. For this reason Vrf is made small and one can find betatron tunes where neither instability manifests itself. For example, the working point is located between high order synchrotron-betatron resonances 2QX — 10Q* = 1 and 2QX — 12Q* = 1. At low energies beamstrahlung leads to a significant increase in the energy spread and, correspondingly, the bunch lengthening. If Np is large enough to achieve high £*, then az becomes several times larger; in this case it scales as az « /Np. Accordingly, C* and luminosity also grow « -y/Np while £X remains constant. This means that increasing Np does not reach the instability threshold, but only increase the energy spread. In general, Np can be limited by several factors: £*, beam lifetime (depends on the energy spread and energy acceptance), and the impedances. The result is close to all these limits, which corresponds to a full exploitation of the available margins. Optimisation at the WW threshold As the energy increases to ^80 GeV, aX grows due to the synchrotron radiation and the bunch lengthening due to the beamstrahlung decreases, therefore the Piwinski angle drops. In addition, the damping decrement grows with 73. All this leads to an increase in the instability threshold. For example, at W± it is already possible to work in a lattice with small momentum compaction. However, there is one more important requirement: in order to obtain a resonant depolarisation, which is neces- sary for the energy calibration, the synchrotron tune Q* must be larger than 0.025 (see Sect. 2.7). To achieve such a Q* value, the momentum compaction has to be increased. Therefore, the same 60°/60° lattice was chosen as for Z. Furthermore, the RF voltage must be increased to 750 MV, so the only window for a good working point can be found between 2QX — 4Q* = 1 and 2QX — 6Q* = 1. In order that insta- bilities do not arise near these resonances, ß* < 20 cm is required. Here it should be noted that with increasing energy, obtaining small beta functions becomes more difficult as this leads to a reduction in the dynamic aperture and momentum accep- tance. Consequently, ß* was increased to 1 mm. To obtain the higher Vrf required, the single-cell cavities used at Z will be replaced by multi-cell ones, whose capacity to damp the higher order modes (HOM) is limited. An important consequence is that the number of bunches should not be smaller than 2000 and, therefore, the luminosity at W± is limited by this factor. The possibility of increasing Q* further to 0.0375 at W± was also considered, in accordance with the desire to improve the conditions for resonant depolarisation. In this case QX falls between low order resonances 2QX — 2Q* = 1 and 2QX — 4Q* = 1. To avoid coherent instabilities it is necessary to reduce ßX* to 15 cm. The momentum acceptance drops accordingly and, as a consequence, luminosity decreases. On the other hand, the number of bunches for this option is larger (2500), though they are shorter. This option is not worse for HOM and the luminosity is about the same as for 2000 bunches with Q* = 0.025. However, obtaining Q* = 0.0375 would require twice the RF voltage VRF and, thereby, a revised RF staging scenario. Therefore, the current baseline is Q* = 0.025. Optimisation at the ZH cross-section maximum Polarisation is not an issue at a beam energy of 120 GeV (ZH production) and the optimum parameters are selected as follows: 330 The European Physical Journal Special Topics 1. The 90°/90° lattice, which provides naturally smaller emittances. 2. The RF voltage is made as small as possible, but adjusted so that the RF accep- tance (bucket height) is larger than the energy acceptance due to dynamic aper- ture, resulting in Q* « 0.018. 3. QX is selected in the range of 0.56-0.58 with the condition that QX « 0.5 + Q* • (m+0.5) in order to be separated from the low-order synchro-betatron resonances and Q* = QX+ (0.03-0.04). 4. A ß* at which the coherent instabilities disappear is then sought; in this case, 30 cm is enough. 5. With the given ex and ß*, the length of interaction area Lj « 0.9 mm, and this defines the optimum ß*. However, obtaining small ß* at higher energies is more difficult, so 1 mm was chosen. 6. The lattice optimisation was performed for the selected ß* in order to maximise the dynamic aperture and energy acceptance. 7. A fine scan of betatron tunes was performed to choose the working point more precisely. 8. Then quasi-strong-strong beam-beam simulations were performed with an asym- metry of 3% in the bunch currents (3% is determined by the required beam lifetime and the injection cycle time). At energies W±, ZH, and tt, single high- energy beamstrahlung photons become important and impose a limit on Np. The bunch population is scanned, while the restriction is the lifetime of the weak (less populated) bunch. The maximum and luminosity are determined in this way. Optimisation at the tt threshold and above At the tt production (beam energy from 170 to 182.5 GeV) the coherent instabilities are suppressed by very strong damping, but another problem becomes dominant: the lifetime limitation by single high-energy beamstrahlung photons [168]. Thus, in contrast to low energies, ß* should be increased in order to make ax larger and thereby weaken the beamstrahlung. With increased ax, Lj « 1.8 mm is obtained, and ßy* should be about the same (or slightly smaller). It should be noted that an increase in ex is not profitable since a small ey is needed for high luminosity, so the 90°/90° lattice is used. 2.3 Design challenges and approaches Based on combinations of existing technologies for e+e- circular colliders developed through the last half century, the FCC-ee will achieve the best ever luminosities at each energy. Although some components need final touches to their design or proto- typing in the phase after the CDR, the fundamental feasibility of their construction has already been proven in other colliders and storage rings. 2.3.1 Synchrotron radiation The synchrotron radiation (SR) is a key feature for any e+e- storage ring. It is worth comparing the characteristics of FCC-ee with those of LEP2, the highest energy e+ e- ring ever operated and PEP-II high energy ring, one of the e+e- colliders with the highest beam current (see Tab. 2.2). While the total radiation power is higher than that of LEP2 by a factor of 4, the critical energy and the energy loss per arc length are only 20% and 10% higher, FCC-ee: The Lepton Collider 331 respectively. The power dissipation per arc length is less than 1/4 of that at PEP-II. The level of synchrotron radiation can therefore be handled by existing technology. Another aspect of the SR is the radiation towards the detector at the IP. This issue is addressed by the beam optics around the IP which limits the critical energy of the SR photons from the dipoles upstream of the IP to below 100 keV [162], from ~480m from the IP. The highest critical energy of photons experienced at LEP2 was 83keV at ~270m from the IP [174]. Thus the criterion for FCC-ee sounds reasonable. The suppression of the SR towards the IP is achieved by asymmetric beam optics around the IP. The detailed analysis of the effect of SR for the detector is given in Section 2.5. 2.3.2 Tapering The tapering method is essential to maintain the beam orbit and the optics at the design values with the high synchrotron radiation loss around the ring, especially at tt. Here it is assumed that all dipoles and quadrupoles have independent trim windings to facilitate the tapering [162]. Sextupoles are paired more or less locally and have independent power supplies. The magnitude of the trims reaches ±1.2% near the RF cavities. These trim windings are also useful for the correction of the orbit and the beam optics. While most of the dipoles and quadrupoles use the “twin aperture” scheme described below, trim windings can be installed independently for the two beams. 2.3.3 Dynamic aperture, beam lifetime, top-up injection The FCC-ee will be the first circular collider where beamstrahlung dominates the luminosity performance. Thus the first requirement is that the collider optics must have sufficiently large dynamic momentum acceptance to hold a particle that loses its energy in a single photon emission due to beamstrahlung. The second requirement arises because beamstrahlung also increases the equilibrium momentum spread of the beam by multiple random emissions of photons, therefore the dynamic momen- tum aperture must ensure the quantum lifetime [175]. Generally speaking, at higher energy such as tt, the first effect is more critical than the second one. The dynamic aperture must be large enough to capture the injected beam for the top-up injection. There are at least two schemes: off-axis-on-momentum and on-axis- off-momentum injections. They need transverse on-momentum or off-momentum dynamic apertures, respectively. The dynamic aperture of the optics that has been designed is sufficient for both injection schemes at all energies [176]. There are two major processes which determine the beam lifetime. One is the radiative Bhabha scattering at the IP, which is proportional to the luminosity divided by the number of particles stored in the ring. The other is the lifetime given by the beamstrahlung and the dynamic momentum acceptance. The latter depends on the optimisation of the beam parameters as discussed in the previous section. The resulting lifetime, as shown in Table 2.1, matches the capacity of the injector. The injection must be done with a “bootstrap” procedure, in which the imbalance of the charges of both beams is kept within a certain relative difference, i.e. ±5% at Z and ±3% at higher energies, as described in the previous section. 2.3.4 Low emittance tuning and optics correction To maintain the vertical emittance ey below the design criteria is also necessary to reach the higher luminosity, as well as being important to ensure beam polarisation 332 The European Physical Journal Special Topics Table 2.1. Machine parameters of the FCC-ee for different beam energies. Z WW ZH tt Circumference (km) Bending radius (km) Free length to IP t (m) Solenoid field at IP (T) Full crossing angle at (mrad) IP 9 SR power / beam (MW) 97.756 10.760 2.2 2.0 30 50 Beam energy (GeV) 45.6 80 120 175 182.5 Beam current (mA) 1390 147 29 6.4 5.4 Bunches / beam 16640 2000 328 59 48 Average bunch spac- ing (ns) 19.6 163 994 2763a 3396a Bunch population (10n) 1.7 1.5 1.8 2.2 2.3 Horizontal emittance (nm) 0.27 0.84 0.63 1.34 1.46 Sx Vertical emittance sy (pm) 1.0 1.7 1.3 2.7 2.9 Arc cell phase advances (deg) 60/60 90/90 Momentum com- paction ap (10-6) 14.8 7.3 Arc sextupole fami- lies 208 292 Horizontal ßX Vertical ßX (m) (mm) 0.15 0.8 0.2 1.0 0.3 1.0 1.0 1.6 Horizontal size at IP (p m) 6.4 13.0 13.7 36.7 38.2 Vertical size at IP aß (nm) 28 41 36 66 68 Energy spread (SR/BS) a (%) 0.038/0.132 0.066/0.131 0.099/0.165 0.144/0.186 0.150/0.192 Bunch length (mm) (SR/BS) az 3.5/12.1 3.0/6.0 3.15/5.3 2.01/2.62 1.97/2.54 Piwinski angle (SR/BS) ß 8.2/28.5 3.5/7.0 3.4/5.8 0.8/1.1 0.8/1.0 Length of interaction (mm) area Li 0.42 0.85 0.90 1.8 1.8 Hourglass factor -Rhg 0.95 0.89 0.88 0.84 0.84 Crab sextupole strength6 (%) 97 87 80 40 40 Energy loss / turn (GeV) 0.036 0.34 1.72 7.8 9.2 RF frequency (MHz) 400 400 / 800 RF voltage (GV) 0.1 0.75 2.0 4.0 / 5.4 4.0 / 6.9 Synchrotron tune Qs 0.0250 0.0506 0.0358 0.0818 0.0872 Longitudinal damp- ing time (turns) 1273 236 70.3 23.1 20.4 RF bucket height (%) 1.9 3.5 2.3 3.36 3.36 Energy acceptance (DA) (%) ±1.3 ±1.3 ±1.7 -2.8 +2.4 Notes. (a)A half ring is filled with the common RF scheme. (b)Relative to the geometrical strength k2 = (9xßxßy,sext) \/ßX/ßx,sext. FCC-ee: The Lepton Collider 333 Table 2.1. (Continued.) Z WW ZH tt Polarisation time tp (min) 15000 900 120 18.0 14.6 Luminosity / IP (1034/cm2s) 230 28 8.5 1.8 1.55 Horizontal tune Qx Vertical tune Qy 269.139 269.219 269.124 269.199 389.129 389.199 389.108 389.175 Beam-beam £x/£y 0.004/0.133 0.010/0.113 0.016/0.118 0.097/0.128|0.099/0.126 Allowable e+e- (%) charge asymmetry ±5 ±3 Lifetime by rad. (min) Bhabha scattering 68 59 38 40 39 Actual lifetime due (min) to beamstrahlung > 200 > 200 18 24 18 Table 2.2. Comparison of synchrotron radiation between FCC-ee, LEP2 [173], and PEP- II [173] at their highest energies. FCC-ee LEP2 PEP-II (high energy ring) Highest beam energy (GeV) 182.5 104.6 9.0 Bending radius (km) 10.760 2.584 0.167 Synchrotron radiation loss per turn (GeV) 9.05 4.07 0.0034 Critical energy in the arc dipole (MeV) 1.06 0.83 0.0082 Beam current / species (mA) 5.5 3 1960 Radiation power per beam (MW) 50 12.2 6.8 Total radiation power per arc length (kW/m) 1.2 1.1 5.5 at Z and W±. It is assumed that the emittance ratio is e*/eX > 0.2% and that e* > 1 pm at all energies. The latter condition is important since the vertical emittance generated by the fringe field of the solenoids together with the crossing angle reaches 0.2 pm at Z, where the effect is the largest. The tuning scheme described later uses skew quadrupole fields generated by trim windings on arc sextupoles to control the vertical emittance generated by the misalignments in the arc. The x—y coupling and dispersion can be measured using beam position monitors (BPMs) at each quadrupole in either a turn-by-turn or multi-turn mode. The method resembles those developed at other colliders such as LHC and B factories, as well as those used at light sources. The misalignment tolerances and the precision of the diagnostics is comparable to those that have been achieved in the aforementioned machines. Special care will be needed for the error correction of the final focus quadrupoles and the local chromaticity section, where the ß functions assume high values of up to 6 km. The correction of the beam optics including the ß-functions and horizontal dis- persion will be important for both the low emittance tuning and the dynamic aper- ture. The trim windings on all of the quadrupoles equipped for tapering will also be used for optics corrections. 2.4 Optics design and beam dynamics 2.4.1 Lattices The beam optics was established for the baseline in 2016 [162], then further revised [177,178] so as to include several modifications such as 60°/60° phase advance at 334 The European Physical Journal Special Topics Fig. 2.4. Cross-section of the tunnel in the arc region. The dual-aperture magnets of the collider ring are located towards the outside of the ring tunnel (left), with the magnets of the booster more towards the inside of the ring tunnel (middle). A magnet installation vehicle travels along the transport passage. Z and WW, twin-aperture quadrupoles [24], a section for inverse-Compton spec- trometer [179], etc. In the following description, the beam energy at tt is 182.5 GeV, unless specified otherwise. The arc optics are based on FODO cells with either 90°/90° (ZH and tt) or 60°/60° (Z and WW) phase advance. A FODO cell has the best packing fac- tor of dipoles, which is a crucial condition for a high energy collider. Since twin- aperture quadrupoles are used, both horizontally focusing (QF) and defocusing (QD) quadrupoles must have the same length, thus the spacing between quadrupoles must be the same. The number of cells was chosen such that the target horizontal emittance could be achieved. Generally speaking, although an even smaller emittance may be favourable for higher luminosity, it requires a still shorter cell length. A shorter cell reduces the horizontal dispersion and the momentum compaction factor. As a result, the quadrupole and sextupole magnets become stronger and longer, which degrades the dipole packing factor. A smaller momentum compaction can also lead to beam instabilities due to single-beam collective effects and due to the beam-beam effect. In addition, a shorter quadrupole magnet with a stronger field will degrade the dynamic aperture due to the synchrotron radiation. Thus, the current number of FODO cells is already close to the maximum. The resulting packing factor of dipoles in the arc is 81.8%. Figure 2.4 shows the tunnel cross-section with magnets installed. Trim windings on sextupole magnets will be used as horizontal/vertical dipole and skew quadrupole correctors to avoid the need for dedicated correctors, thereby improving the packing factor. Using a combined function dipole may have benefits for the emittance and momentum compaction factor by increasing the horizontal FCC-ee: The Lepton Collider 335 Fig. 2.5. Three magnet arrangements around a quadrupole. D: twin-aperture dipole, Q: twin-aperture quadrupole. S: single-aperture sextupole. (A) no sextupole, (B) single aper- ture, singlet sextupole only for 60°/60°, (C) single aperture, doublet sextupole for either 60°/60° or 90°/90°. In case (C) for 60°/60°, only the part of the doublet next to the quadrupole is powered. As a result, three dipole lengths are needed to maintain a constant distance between quadrupoles. damping partition, but the resulting momentum spread is not suitable for polarisa- tion and this option has therefore been rejected. Non-interleaved families of sextupole pairs, with a —I transformation between sextupoles [180], are placed in the FODO cells. As the phase advance is different between high and low energies, the locations of the usable sextupoles depend on the mode of operation. There are three types of the arrangement of a sextupole around a quadrupole as shown in Figure 2.5: no sextupole, a singlet sextupole, and a doublet sextupole. Whilst a doublet is used at higher energies, only one of the two sextupoles is used at lower energies, if the optics requires a sextupole field at that location. A singlet sextupole is installed where a sextupole is only needed at the lower energy. To achieve a better dipole packing factor where possible, the spaces not needed for a sextupole are filled with dipoles. Thus, there are three dipole lengths but with the same bending radius. The resulting lattice has a super period of 35 FODO cells as shown in Figure 2.6. Within the super period, the ß-functions are almost periodic in each cell, since the focusing due to dipoles is weak. On the other hand, the horizontal dispersion has a modulation within a super period. Studies of the effect of such a modulation on the dynamic aperture have so far not shown any negative effect. All sextupole pairs are independently powered. There are 294 and 208 independent pairs per half ring for 90°/90° and 60°/60°, respectively. The non-interleaved scheme of sextupoles has been applied at B-factories and successfully operated for more than 15 years [181,182]. At KEKB, the number of pairs was 52 per ring. 2.4.2 Interaction region One of the beam optics challenges for the collider is providing an adequate dynamic aperture with small ß-functions down to ßj y = (0.15 m, 0.8 mm) at the interaction point, for operation on the Z pole. Although these values are still higher than those in modern B factories [183], the associated vertical chromaticity around the IP is comparable, since the distance, f* , from the face of the final quadrupole magnet to the IP is longer than those in the B factories. Also, especially at the tt energy, the beamstrahlung caused by the collisions requires a very wide momentum acceptance of —2.8% + 2.4%. The transverse on-momentum dynamic aperture must be larger than ~12aæ to enable top-up injection in the horizontal plane. 336 The European Physical Journal Special Topics Fig. 2.6. The beam optics of the arc super cell of FCC-ee, for two phase advances. Left: 90°/90° (for ZH and tt) right: 60°/60° (for Z and WW). The upper and lower rows show /ßx,y and dispersions, respectively. The locations of the focusing and defocusing sextupoles, SF and SD, are indicated by red and blue arrows, respectively, for each phase advance. Every two sextupoles are paired with a —I transformation between them. Figure 2.7 shows the optics in the interaction region (IR) for tt. It has a local chromaticity correction system (LCCS) only in the vertical plane at each side of the IP. The sextupole magnet pairs for the LCCS have one at each side of the IP and only the inner ones at (b,c) have non-zero horizontal dispersion [184]. The outer ones at (a,d) perform two functions: cancelling the geometrical nonlinearity of the inner ones and generating the crab waist at the IP; in order to accomplish the second function the (a,d) phase advance from the IP is chosen as A/X,* = (2n, 2.5n), as described in [162]. The incorporation of the crab sextupoles into the LCCS saves space and reduces the number of optical components. The optimum magnitude of the sextupole depends on the luminosity optimisation. As the crab sextupoles are dispersion-free [184], they can be adjusted to any ratio up to the “full crab waist” without causing unnecessary side effects. The beam lines in the interaction region are separate for the two beams and there are no common quadrupoles in the IR. As a baseline f* is chosen to be 2.2 m [185], which is sufficient for two independent final quadrupoles with a 30 mrad crossing angle. The detector solenoids are common to the two beams and their effects are compensated locally with counter solenoids, which cancel the f dz between the IP and the faces of the final quadrupole, as shown in Figure 2.8. The vertical orbit, vertical dispersion, and x—y couplings do not leak out for any off-momentum par- ticles. The vertical emittance increases due to the fringe field of the compensating solenoid combined with the horizontal crossing angle. The increase becomes largest at the Z energy as the solenoid field is independent of the beam energy. The increase of the vertical emittance is below 0.4 pm for 2 IPs. A realistic profile of shown in Section 2.5. The optimised ß* * discussed in Section 2.2 is smaller at lower beam energies. To reduce ß* at the Z from ß* * = (1m, 1.6mm) at tt to (0.15 m, 0.8 mm) at Z, the vertical focusing quadrupole in the final focus which is closest to the IP (know as QC1), which is located at f* = 2.2m from the IP, is split into three pieces. The polarities and the strengths of these pieces depend on the beam energy. For instance, all three pieces provide vertical focusing at tt, and only the first piece provides vertical focusing while the remaining two focus horizontally at Z. The field strengths are limited to the same value, 100 T/m, at all beam energies. With this triple splitting, the centre of focusing for each plane moves closer towards the IP at the Z, which reduces the increment of the chromaticity for the smaller ß*. Comparing FCC-ee: The Lepton Collider 337 Fig. 2.7. The beam optics of the FCC-ee IR for tt. Upper and lower rows show ffßx,y and dispersions, respectively. The beam passes from the left to the right. The optics is asymmetric to suppress the synchrotron radiation toward the IP. Dipoles are indicated by yellow boxes; those in region (e) have a critical energy of the SR photon below 100 keV at the tt. Sextupoles for the LCCS are located at (a-d), and sextupoles at (a,d) play the role of crab sextupoles. left and right of Figure 2.8, it can be seen that the beam sizes at Z through this region are still smaller than those at tt. The peak value of ßy is almost unchanged even though ßy is reduced by a factor of 2. The peak of ßx at Z is about 3 times higher, while ß*x becomes 1/6 of the value at tt. The critical energy of SR photons from the dipoles up to 500 m upstream of the IP is set below 100 keV at tt. There are no dipole magnets upstream of the IP for up to 100 m. 2.4.3 RF section and other straight sections Figure 2.9 shows the beam optics for the half ring for tt. The RF sections are located in the long straight sections around PJ and PD as shown in Figure 2.1. At tt, an acceleration voltage of ~5.3GV per section is needed; As a result, the length of the RF installation for the collider will be about 1 km (with a similar length for the top-up booster). At the tt energy, both beams pass through a common RF section. A combination of electrostatic separators and a dipole magnets deflects only the outgoing beam so at to avoid any SR shining towards the RF cavities. In this running mode, the quadrupoles within the RF section are common to both beams, but they are still compatible with the overall tapering scheme, if their strengths are symmetrical about the mid-point of the RF section. 338 The European Physical Journal Special Topics Fig. 2.8. The yjßx,y and beam sizes around the IP at Z (upper left), WW (upper right), ZH (lower left), and tt (lower right). The beam sizes assume the equilibrium emittances listed in Table 2.1. The final quadrupoles QC1(L/R) are longitudinally split into three slices. While all slices of QC1 are vertically focussing at tt, only the first ones are at Z. Note that the inner radius of the beam pipe through these quadrupoles is larger than 15 mm. The staging of the RF system adds cavity modules step by step as the energy increases, starting at Z up to tt. The beam line in the RF section needs minimal modification as more modules are installed. Most of the RF cavities and cryomodules are reused at the various stages. Figure 2.10 depicts the tunnel cross section with the installed RF system. The straight section (a) in Figure 2.9 has space for a spectrometer which will use inverse Compton scattering from a laser to measure the beam energy and the polarisation. This section has a free space of 100 m immediately after the dispersion suppressor dipole at the entrance of the inner ring and therefore the beam optics is different to that of (b). The remaining straight sections will be used for injection, beam dump and collimation. 2.4.4 Dynamic aperture The dynamic aperture (DA) has been estimated using the computer code SAD [186], taking into account the effects listed in Table 2.3. The synchrotron radiation from the dipoles improves the aperture, especially at tt, due to the strong damping, whereas the radiation loss in the quadrupoles for particles with large betatron amplitudes reduces the dynamic aperture. This is due to the synchrotron motion induced by the radiation loss as described in reference [162]. This effect is most noticeable in the horizontal arc quadrupoles; therefore, the length of the arc quadrupoles must be sufficiently long. The final focus quadrupole has another effect resulting from the SR which makes the transverse damping unstable. The vertical motion for a FCC-ee: The Lepton Collider 339 Fig. 2.9. The beam optics of the FCC-ee half ring for tt. Upper/lower plots show ffßx,y and horizontal/vertical dispersions, respectively. These plots start and end in the middle of the RF sections, and the IP is located at the centre. Sections marked by (a,b) correspond to the intermediate straight sections PB, PF, PH, PL in Figure 2.1. Fig. 2.10. Tunnel cross section with radiofrequency equipment installed (collider main ring in red and booster ring in green). An RF unit being installed is shown in blue. The grey equipment represents the cryogenic distribution line. 340 The European Physical Journal Special Topics Table 2.3. Effects taken into account during the optimisation of the dynamic aperture. Effect Significance Synchrotron motion Radiation loss in dipoles Radiation loss in quadrupoles Radiation loss in sextupoles Tapering Crab waist Maxwellian fringes [187] Kinematic terms Essential Essential - improves the aperture, esp. at ZH and tt Essential - reduces the aperture Minimal Essential Transverse aperture is reduced by ~20% for 100% strength Small Small Fig. 2.11. Dynamic apertures in z—x plane after sextupole optimisation with particle tracking for each energy. The initial vertical amplitude for the tracking is always set to Jy/ Jx = ey/ex. The number of turns corresponds to about 2 longitudinal damping times. The resulting momentum acceptances are consistent with the luminosity optimisation shown in Table 2.1. Effects in Table 2.3 are taken into account. The momentum acceptance at tt is “asymmetric” to match the distribution with beamstrahlung. ß* = 0.8 mm at Z is unstable for Ay > 30