Gravitational Waves from Phase Transition in Minimal SUSY $U(1)_{B-L}$ Model

TL;DR

This paper investigates gravitational wave production from a high-scale phase transition in a minimal supersymmetric $U(1)_{B-L}$ model, deriving the effective potential and estimating the resulting stochastic gravitational wave signals.

Contribution

It provides the first detailed analysis of gravitational waves from $U(1)_{B-L}$ symmetry breaking within a SUSY framework in the SUSY limit.

Findings

Phase transition can produce detectable gravitational waves in ground-based detectors.

Finite temperature effective potential for the SUSY $U(1)_{B-L}$ model is derived.

Estimates show gravitational wave signals are within the sensitivity of future experiments.

Abstract

Many extensions of the Standard Model include a new $U(1)$ gauge group that is broken spontaneously at a scale much above TeV. If a $U(1)$-breaking phase transition occurs at nucleation temperature of $O(100)$-$O(1000)$~TeV, it can generate stochastic gravitational waves in $O(10)$-$O(100)$ Hz range if $\beta_{\rm n}/H_{\rm n}=1000$, which can be detected by ground-based detectors. Meanwhile, supersymmetry (SUSY) may play a crucial role in the dynamics of such high-scale $U(1)$ gauge symmetry breaking, because SUSY breaking scale is expected to be at TeV to solve the hierarchy problem. In this paper, we study the phase transition of $U(1)$ gauge symmetry breaking in a SUSY model in the SUSY limit. We consider a particular example, the minimal SUSY $U(1)_{B-L}$ model. We derive the finite temperature effective potential of the model in the SUSY limit, study a $U(1)_{B-L}$-breaking phase transition, and estimate gravitational waves generated from it.