Scattering Entanglement Entropy and Its Implications for Electroweak Phase Transitions

Abstract

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 $O(N)$ real singlet scalars $S$ via the Higgs portal coupling $λ_{hS}$. By explicitly calculating the maximum entanglement entropy, we demonstrate that it grows with increasing $λ_{hS}$, 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.

Figures (6)

• Figure 1: $x$ and $y$ dependence for the function $G(x,y)$.
• Figure 2: Energy dependence of the entanglement power in the $O(N=4)$ singlet models with $m_{S}=500\,{\rm GeV}$ for fixed $\lambda_{hS}$ and $\lambda_{S}$.
• Figure 3: Maximal entanglement entropy in ($\lambda_{hS}, \lambda_{S}$) plane for each benchmark point. The black dashed and dotted lines indicate the boundary for the sFOEWPT shown in Eq. \ref{['eq:vcTc1']} and FOEWPT given in Eq. \ref{['eq:fopt']}, respectively. The light gray region (PUB) is constrained by the perturbative unitarity bound in Eq. \ref{['eq:unitarity']}. In the white region, the requirement $\mu_{S}^2 >0$ cannot be satisfied. The dark gray region is constrained by the requirement that the phase transition should be completed within the age of the universe Turner:1992tz.
• Figure 4: The maximal entanglement power in $(\lambda_{hS}, m_{S})$ plane. The gray region is constrained by the perturbative unitarity \ref{['eq:unitarity']}. In the lower right region below the black dashed lines, the sFOEWPT can be realized.
• Figure 5: The maximal entanglement power in $(\lambda_{hS}, v_{h})$ plane. When the FOEWPT occurs ($\braket{\phi} = 0 \to \braket{\phi} \neq 0$), the discontinuous production of entanglement entropy occurs. The gray region is constrained by the perturbative unitarity bound given in Eq. \ref{['eq:unitarity']}. In the case with $m_{S} =500\,{\rm GeV}$, the condition $\mu_{S}^2 \geq 0$ is always satisfied in the parameter region on which we focus.