SEARCH FOR DEEPLY BOUND KAONIC NUCLEAR STATES IN THE AMADEUS EXPERIMENT ∗

We brieﬂy report on the search for Deeply Bound Kaonic Nuclear States with AMADEUS in the Σ 0 p channel, and future perspectives.


Introduction
The existence or not of the Deeply Bound Kaonic Nuclear States (DBKNS) is currently one of the hottest topics in nuclear and hadronic strangeness physics, both from experimental and theoretical points of view. The existence of bound kaonic nuclear states of K − , also called kaonic nuclear clusters, was firstly predicted in 1986 [1]. The position of the Λ(1405) reflects the strength of theKN interaction, thus influencing the possible formation of K multi-nucleon bound states. Accordingly, recent theoretical calculations, based on different approaches, deliver a wide range of bindings and widths for the di-baryonic kaonic bound state ppK − [2][3][4][5][6][7], while the experimental results are contradictory [8][9][10][11][12][13][14]. Moreover, the extraction of a ppK − signal in K − absorption experiments is strongly affected by the yield and the shape of the competing K − multi-nucleon absorption processes. Therefore, in order to clarify this issue, experimental data are needed. This research is very important in understanding the fundamental laws of the Nature and Universe. It can have important consequences in various sectors of physics, such as nuclear and particle physics, as well as astrophysics. The binding of the kaon in nuclear medium may have impact on models describing the structure of neutron stars (Equation of State of neutron stars) [15,16] including binaries which are expected to be sources of the gravitational waves. Investigation of stable forms of strange matter like DBKNS in extreme conditions would be helpful for a better understanding of elementary kaon-nucleon interaction for low energies in the non-perturbative quantum chromodynamics (QCD) and would contribute to solving crucial problems in hadron physics: hadron masses (related to the chiral symmetry breaking), hadron interactions in nuclear medium and the structure of the dense nuclear matter.
The AMADEUS group has developed a method having a high chance for a discovery of DBKNS corresponding to K − pp, K − ppn and K − ppnn kaonic nuclear clusters and their decays to Σ 0 /Λp, Σ 0 /Λd and Σ 0 /Λt, respectively. The method is based on the exclusive measurement of the momentum, angular and invariant mass spectra for correlated Σ 0 /Λp, Σ 0 /Λd, Σ 0 /Λt pairs [17]. Possible DBKNS may be produced with K − stopped in helium or carbon and then decaying into considered decay channels. The AMADEUS experiment is conceived to perform a systematic investigation of the low-energyKN interaction, taking advantage of the kaon beams delivered by the DAΦNE collider [18]. The ongoing AMADEUS analyses refer to two data samples. One is represented by the data collected by the KLOE Collaboration [19] during the 2004/2005 data taking, corresponding to ∼ 1.74 fb −1 . The KLOE detector [20] is used as an active target, the hadronic interaction of negative kaons with the materials of the apparatus being investigated. This includes, in particular, K −9 Be absorptions in the DAΦNE thin beryllium cylindrical layer and the DAΦNE aluminated beryllium pipe, K −12 C and K − H absorptions in the KLOE Drift Chamber [21] (DC) inner wall (aluminated carbon fiber), and K −4 He in the DC gas. Extremely rich experimental information is contained in this sample, with K − hadronic captures both at rest and in flight [22]. In order to increase the statistics, a high purity carbon target (graphite) was realized in the summer of 2012 and installed inside the KLOE detector, between the beam pipe and the DC inner wall. This setup is crucial because it serves as an essential interpretation tool. The geometry of the target was optimized to maximize the kaon stopping power. The total collected integrated luminosity is ∼ 90 pb −1 . Up to now, we analysed a sample of 37 pb −1 reconstructed data. The adopted procedure is to exclusively measure the correlated Σ 0 /Λp, Σ 0 /Λd and Σ 0 /Λt pairs, searching for the production of K − pp , K − ppn and K − ppnn multi-nucleon, and related bound states. In the next section, we briefly present the results of data analysis devoted to the Σ 0 p channel. A detailed description can be found in Ref. [23].

Σ 0 p data analysis
The analysis presented below is focused on studies of K − absorption processes inside the DC carbon wall leading to the Σ 0 p final state [23]. Selection of Λ(1116) hyperons, being the signature of the K − hadronic interaction in 12 C, was the first aim of the data analysis. Λs were identified via reconstruction of their decay vertex Λ → p + π − (BR = 63.8%). The selection and identification of protons and negatively charged pions was done using the dE/dx information in the DC installed around the interaction point and the momentum of the track. The proton-pion invariant mass was determined under the p and π − mass hypothesis. The constructed pπ − invariant mass resulted in a value of 1115.753 ± 0.002 MeV/c 2 and a statistical error of 0.5 MeV/c 2 . Then, the Λ-proton vertex was searched for, and K − absorption processes inside the DC wall were selected based on the radial position ρ Λp . The identification of Σ 0 candidates was carried out through their decay into Λγ pairs, where γ quanta were identified in calorimeter [24]. Afterwards, a simultaneous global fit to the Σ 0 p invariant mass, the cos(θ Σ 0 p ), the Σ 0 and the proton momenta was performed in order to extract contributions from the different absorption processes like 2-Nucleon Absorption (2NA) with final-state interaction (FSI) or without it (QF), 3NA and 4NA. For this purpose, Monte Carlo simulations of the absorption processes in 12 C were carried out. The final fit is presented in Figs. 1 and 2. It determined the contribution of the different absorption processes. The fit results in the first measurement of the 2NA free from FSI, which was found to be 12% of the total absorption cross section. Contribution from the K − pp bound state was included in the second fit of the experimental data. A Breit-Wigner shape was used to simulate the bound state contribution, scanning a grid of possible bindings (15-75 MeV/c 2 in steps of 15 MeV/c 2 ) and widths (30-70 MeV/c 2 in steps of 20 MeV/c 2 ). The best value of the total reduced χ 2 was achieved for the hypothesis of a binding energy of 45 MeV/c 2 and width 30 MeV/c 2 , as shown in Fig. 3. The K − pp yield extracted from the fit is However, an F-Test was carried out to compare the two models (with and without a K − pp bound state) results in a 1σ significance for the best fit which does not allow to claim the observation of a bound state. For what concerns the distributions, the systematic errors are also evaluated for um momentum of the nucleons required to exit the nue absorption simulation and the probability of having one collision when simulating the FSI with the residual llowing a 2NA process. inimum momentum for the nucleons is sampled acthe Fermi momentum distribution between 170 and c. The systematic error is evaluated by varying the two s by 15% in both directions. For the systematic variation bability of having one or two collisions for the FSI proases, 40/60% and 60/40%, are evaluated respectively. al fit results deliver the contribution of the different o the analysed 0 p final state. The best fit delivers a f 0.85. The emission rates extracted from the fit are Table 1 Production probability of the 0 p final state for different intermedia normalised to the number of stopped K − in the DC wall. The statistical atic errors are shown as well. "Tot 2NA" stands for the sum of the 2NA 2NA-FSI processes. "Tot 3 body" stands for the sum of 2NA-FSI and 3NA Similar measurements have been carried out and re [9,20]. In [9] stopped K − in a 4 He target have been consid the integrated contribution to the final state 0 ( ) wit emission was extracted and found to be equal to 0.11 per stopped K − . This large number is due to the conta in the sample and to the fact that absorptions on p-n included. The data in [20] show the measurement of th nal state from a 13 C target. There, a yield of 0.  Similar measurements have been carried out and rep [9,20]. In [9] stopped K − in a 4 He target have been consid the integrated contribution to the final state 0 ( ) with emission was extracted and found to be equal to 0.117 per stopped K − . This large number is due to the conta in the sample and to the fact that absorptions on p-n p included. The data in [20] show the measurement of the nal state from a 13 C target. There, a yield of 0.46 ± 0.09 0.02(syst) · 10 −2 per stopped K − is attributed to the K − ab      ditional fit parameter, by comparing the residuals and num degrees of freedom of two models. The resulting F value re follows: sts were performed that demonstrate that both physical es should be included in the fit. First, if the 3NA contriis switched off a variation of the reduced χ 2 of 0.19 from he best fit) to 1.05 is observed. Such effect is mainly due fact that the 0 and the proton momentum distributions longer well described. The other kinematic distributions are nsitive to this contribution. In particular, the χ 2 calculated fit result of the proton momentum distribution only is deted by 47% when excluding the 3NA contribution from the a second limiting case the 2NA + FSI contribution was dis-, leading to a reduced χ 2 of 1.18. In this case the cos(θ 0 p ) p invariant mass distributions are not properly reproduced. uncorrelated emission of the 0 p is also not distinguishm the 4NA process and hence these two contributions are up.
ch for the ppK − bound state signal last step of the analysis consists in the search of the ound state produced in K − interactions with nuclear tarecaying into a 0 p pair. The ppK − are simulated similarly 2NA-QF process but sampling the mass of the ppK − state Breit-Wigner distribution, rather than the Fermi momenta two nucleons in the initial state. The event kinematic is ented by imposing the momentum conservation of the esidual nucleus system. Different values for the binding end width varying within 15-75 MeV/c 2 and 30-70 MeV/c 2 s of 15 and 20 MeV/c 2 , respectively, are tested. This range cted according to theoretical predictions [14] and taking count the experimental resolution. The global fit is repeated the ppK − state to the processes 1-4. The best fit (χ 2 /ndf = is obtained for a ppK − candidate with a binding energy of V/c 2 and a width of 30 MeV/c 2 , respectively. Fig. 3 shows ults of the best fit for the 0 p invariant mass and proton tum distributions where the ppK − bound state contribution n in green. The resulting yield normalised to the number hows the yield results from the two best fits of the bound ith a width of 30 MeV/c 2 and a binding energy of 45 and

Summary and conclusion
One of the AMADEUS's goals is to search for Deeply Bound Kaonic Nuclear States by studies of K − absorption processes in various tergets. In this work, the investigation of Σ 0 p final state was presented. It results in the extraction of contributions from various few-nucleon absorption processes. Contribution from a possible K − pp bound state was determined, however, the significance of the result is not sufficient to claim the observation of a bound system. Presently, the analysis is in progress for other channels such as Λp, Λd and Λt. Moreover, a feasibility study [25,26] is ongoing for the realization of a dedicated AMADEUS experimental setup, in order to deepen and extend the low-energy anti-kaon nuclei interaction studies and obtain a fundamental input for the understanding of the QCD with strangeness.