In this paper we present prospects for using the J-PET detector to search for
discrete symmetries violations in a purely leptonic system of the positronium
atom. We discuss tests of CP and CPT symmetries by means of ortho-positronium
decays into three photons. No zero expectation values for chosen correlations
between ortho-positronium spin and momentum vectors of photons would imply the
existence of physics phenomena beyond the Standard Model. Previous measurements
resulted in violation amplitude parameters for CP and CPT symmetries consistent
with zero, with an uncertainty of about 10-3. The J-PET detector allows to
determine those values with better precision thanks to a unique time and
angular esolution combined with a high geometrical acceptance. Achieving the
aforementioned is possible due to application of polymer scintillators instead
of crystals as detectors of annihilation quanta.Comment: in Nukleonika 201