Presented at the 5th Jagiellonian Symposium on Advances in Particle Physics and Medicine, Cracow, Poland, June 29–July 7, 2024

The deviations from combined Charge, Parity, and Time (CPT) symmetry could indicate the presence of new physics beyond the current theoretical framework. The positronium (Ps), the lightest bound state of an electron–positron pair, offers a unique probe for such investigations because it is an eigenstate of charge conjugation (C) and parity (P). This work explores the potential of the Jagiellonian Positron Emission Tomography (J-PET) detector for sensitive tests of CPT symmetry in the three-photon decay of ortho-Ps (o-Ps) atom. The CPT symmetry invariance in o-Ps decays has been previously tested using the J-PET detector, measuring the CPT-violating angular correlation between the o-Ps spin and its annihilation photon momenta, achieving a precision of 0.00067 0.00095. However, a range of five orders of magnitude is still unexplored to test its exactness. A Monte Carlo simulation study is presented to distinguish between the o-Ps signal and background events using Multivariate Data Analysis (TMVA). We discuss the impact of improving the sample purity in enhancing the sensitivity of the CPT symmetry test.