Trilateration-based reconstruction of ortho-positronium decays into three photons with the J-PET detector

This work reports on a new reconstruction algorithm allowing to reconstruct the decays of ortho-positronium atoms into three photons using the places and times of photons recorded in the detector. The method is based on trilateration and allows for a simultaneous reconstruction of both location and time of the decay. Results of resolution tests of the new reconstruction in the J-PET detector based on Monte Carlo simulations are presented, which yield a spatial resolution at the level of 2 cm (FWHM) for X and Y and at the level of 1 cm (FWHM) for Z available with the present resolution of J-PET after application of a kinematic fit. Prospects of employment of this method for studying angular correlations of photons in decays of polarized ortho-positronia for the needs of tests of CP and CPT discrete symmetries are also discussed. The new reconstruction method allows for discrimination of background from random three-photon coincidences as well as for application of a novel method for determination of the linear polarization of ortho-positronium atoms, which is also introduced in this work.