Study of certain angular correlations in the three-photon annihilations of the triplet state of positronium, the electron–positron bound state, may be used as a probe of potential CP and CPT-violating effects in the leptonic sector. We present the perspectives of CP and CPT tests using this process recorded with a novel detection system for photons in the positron annihilation energy range, the Jagiellonian Positron Emission Tomography (J-PET). We demonstrate the capability of this system to register three-photon annihilations with an unprecedented range of kinematical configurations and to measure the CPT-odd correlation between positronium spin and annihilation plane orientation with a precision improved by at least an order of magnitude with respect to present results. We also discuss the means to control and reduce detector asymmetries in order to allow J-PET to set the first measurement of the correlation between positronium spin and momentum of the most energetic annihilation photon which has never been studied to dat
