Bell inequalities in 2-2 scattering

Aninda Sinha, Ahmadullah Zahed

Published 2022-12-20Version 1

For 2-2 scattering of photons, gravitons, fermions and pions, we consider entanglement in isospin and helicity. While the photon, graviton and fermion examples involve qubits, pions are qutrits. We calculate the relevant Bell inequalities for these processes. {For photon scattering at low energies, QED lies almost at the theory space boundary which separates the Bell violating theories from the non-violating theories}. Allowing for graviton exchange and demanding Bell violation in photon scattering, we find that the Weak Gravity Conjecture is satisfied. For 2-2 graviton scattering, we find that CEMZ bounds allow for at most small Bell violations. Restriction on the Weinberg angle is found by demanding Bell violation in Bhabha scattering. We use recent S-matrix bootstrap data for pions and photons to study the Bell parameter in the space of allowed S-matrices. In the photon case, we study the Bell parameters as a function of energy and find support for the EFT observations. For pions, we find that there is a minimization of a suitable Bell parameter for S-matrices which exhibit Regge behaviour.