Presented at the Symposium on New Trends in Nuclear and Medical Physics, Kraków, Poland, 18-20 October, 2023.

Positronium is a suitable leptonic system to test Charge-Parity (CP) discrete symmetry involving the correlations of photons momenta originating from ortho-positronium (o-Ps) annihilation. The photon–photon interaction in the final state due to the vacuum polarization may mimic CP symmetry violation of the order of 10, while weak interaction effects lead to a violation of the order of 10 according to the Standard Model prediction. So far, the experimental limits on CP symmetry violation in the o-Ps decay are set at the level of 10. One of the unique features of the J-PET detector is its ability to measure the polarization direction of the annihilation photons without the magnetic field. The J-PET detector can be used to explore discrete symmetry by looking for probable non-zero expectation values of the symmetry-odd operators, constructed from spin of ortho-Positronium and momentum, and polarization vectors of gamma (γ) quanta resulting from o-Ps annihilation. In this work, the J-PET detector experimental and analysis method to improve the sensitivity level at least by one order for CP discrete symmetry studies in the o-Ps decay via symmetry odd operator , where and are reconstructed polarization and momentum vectors of photons from the o-Ps decays, respectively, will be presented.