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Study of certain angular correlations in the three-photon annihilations ofthe triplet state of positronium, the electron-positron bound state, may beused as a probe of potential CP and CPT-violating effects in the leptonicsector. We present the perspectives of CP and CPT tests using this processrecorded with a novel detection system for photons in the positron annihilationenergy range, the Jagiellonian PET (J-PET). We demonstrate the capability ofthis system to register three-photon annihilations with an unprecedented rangeof kinematical configurations and to measure the CPT-odd correlation betweenpositronium spin and annihilation plane orientation with a precision improvedby at least an order of magnitude with respect to present results. We alsodiscuss the the means to control and reduce detector asymmetries in order toallow J-PET to set the first measurement of the correlation between positroniumspin and momentum of the most energetic annihilation photon which has neverbeen studied to date.

Sensitivity of discrete symmetry tests in the positronium system with the J-PET detector