Bell violation in $2\rightarrow 2$ scattering in photon, gluon and graviton EFTs

TL;DR

This paper investigates Bell inequality violations in $2 ightarrow2$ scattering processes within photon, gluon, and graviton EFTs, revealing how initial states and gauge theory types influence entanglement and Bell violation.

Contribution

It demonstrates that Bell violations can occur in scattering processes and distinguishes behaviors between abelian and non-abelian gauge theories and gravity, linking Bell violations to CP properties.

Findings

Bell violation always possible with suitable initial states at some scattering angles.

Non-abelian gauge theories do not exhibit Bell violation within EFT validity for weak couplings.

Bell violation can classify CP-conserving versus CP-violating theories.

Abstract

In this paper, we explore Bell inequality violation for $2\rightarrow2$ scattering in Effective Field Theories (EFTs) of photons, gluons, and gravitons. Using the CGLMP Bell parameter ($I_2$), we show that, starting from an appropriate initial non-product state, the Bell inequality can always be violated in the final state (i.e.,$I_2 >2$) at least for some scattering angle. For an initial product state, we demonstrate that abelian gauge theories behave qualitatively differently than non-abelian gauge theories (or Gravity) from the point of view of Bell violation in the final state: in the non-abelian case, Bell violation ($I_2>2$) is never possible within the validity of EFTs for weakly coupled UV completions. Interestingly, we also find that, for a maximally entangled initial state, scattering can reduce the degree of entanglement only for CP-violating theories. Thus Bell violation in $2\rightarrow2$ scattering can, in principle, be used to classify CP conserving vs violating theories.