  The Positronium (Ps) system, a bound state of an electron and a positron, is
suitable for testing the predictions of quantum electrodynamics (QED), since
its properties can be perturbatively calculated to high accuracy and, unlike
the hydrogen system, is not affected by the finite size or QCD effects at the
current experimental precision level. This makes the Ps atom a good laboratory
to test the Fundamental Symmetries of Physics and also search for new particles
not included in the Standard Model (SM) of physics. On one hand, time reversal
(T) and CP symmetry violation have never been observed in pure leptonic systems
like the Ps atom, and the current experimental limits for CP and CPT violation
in the decays of Ps is currently set at the level of 10^-3, while for C
violation are at the level of 10^-7. These limits are still six and two orders
of magnitude lower than the expected precision of 10^-9 set by photon-photon
interactions. Secondly, experiments searching for invisible decays of the Ps
triplet state, the ortho-Positronium (o-Ps), which mainly decays to three
photons, are being conducted, since they are sensitive to new physics
scenarios, e.g. Mirror Matter (MM), a suitable Dark Matter candidate, proposed
to restore parity (P) violation. By performing a high precision measurement of
the o-Ps lifetime, the accuracy of the present QED calculations can be tested
and a search for the invisible decays of the o-Ps can be performed. These
studies are conducted with the novel total-body Positron-Electron Tomography
(PET) scanner at the JagiellonianUniversity.
