Quantum Gravity Phenomenology and Particle Physics

Quantum gravity phenomenology has been historically regarded as a difficult endeavour, due to the apparent scarcity of phenomena involving the required scales of length (Planck length $l_P$) and energy (Planck energy $E_P$). It was realized, however, that one can look for cumulative effects of a quantum theory of gravity at energies $E/E_P \ll 1$ if even tiny effects are amplified by the large time of flight or very high energies, common to astrophysical phenomena. In the this work, complementary to the COST action CA18108 White Book, we put forward a proposal that quantum gravity phenomenology can be fruitfully pursued also with the help of terrestrial particles accelerators. We first discuss the theoretical background, and then concentrate on deformed discrete symmetries C,P,T. We investigate possible experimental signatures of CPT deformation, particularly concerning the difference in decay time between particles and antiparticles, and fields interference.