Scattering entanglement entropy and its implications for electroweak phase transitions

We investigate the connection between the entanglement entropy in scattering processes and the dynamics of electroweak phase transitions. Recent work has shown that the scattering entanglement entropy can provide new insight into Standard Model parameters. In this study, we propose that the maximum of the entanglement entropy in scattering amplitudes may serve as a diagnostic for first-order electroweak phase transitions in the early Universe. We analyze a simplified extension of the Standard Model consisting of the Higgs boson h coupled to OðNÞ real singlet scalars S via the Higgs portal coupling λhS. By explicitly calculating the maximum entanglement entropy, we demonstrate that it grows with increasing λhS, and that both first-order and strong first-order electroweak phase transitions are favored in regions of parameter space with large maximum entropy. Our results suggest that entanglement-based observables may encode meaningful information about the underlying dynamics of electroweak symmetry breaking and provide a novel perspective on phase transition phenomena.