Test of Space-Time Non-Commutativity at the Future Circular Collider

The Future Circular Collider (FCC) is a crucial step forward to study new Physics beyond the standard model and to test fundamental aspects as space-time minimal length and Lorentz violations. As an example, a possible enhancement of $e^+e^-$ pair production due to non-commutative effects, catalyzed by the huge magnetic field produced at the beginning of a heavy ion collision at FCC, is discussed. In noncommutative electrodynamics a free photon in the magnetic background can produce a $e^+e^-$ pair. In particular for hard photons with transverse energy $100-600$ GeV at the beginning of the collision and for a particular kinematical setting of the pair , i.e. large total transverse momentum in the reaction plane and invariant mass in the range $200-400$ MeV, the non-commutative contribution, evaluated with the present bound of the non-commuativity fundamental area , can be significant. Other, more exotic, possible signatures of space-time non-commutativity are also considered.