Comments on the publication "Discrete symmetries tested at 10e-4 precision using linear polarization of photons from positronium annihilations" by P. Moskal et al

The authors of Ref.[1] (referred to here as "Moskal et al.") claim to have performed the most precise test of P, T and CP invariance in the decay of ortho-Positronium. In this note: 1) we demonstrate, assuming standard properties for Compton scattering, that the average value of the correlation measured by Moskal et al. must necessarily be zero, independently of any physics occurring in o-Ps decay; 2) we point out that there is no formal justification to equate the normal vector to the Compton scattering plane with the incident photon polarization, as done by Moskal et al.; 3) we observe the absence of characterization of the device as a Compton polarimeter, which is paramount in photon polarimetry; 4) we review previous measurements of the polarization of photons from o-Ps decay, properly implementing the Compton polarimetry technique, and make the connection with tests of discrete symmetries; and 5) we stress that the correlation proposed by Moskal et al. cannot be generated solely by the physics of o-Ps decay, including possible violations of discrete symmetries.