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 $O(100)–O(1000)\mathrm{TeV}$, it can generate stochastic gravitational waves in $O(10)–O(100)\mathrm{Hz}$ range if ${\beta }_{\mathrm{n}}/H_{\mathrm{n}}=1000$, 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.

• Received 8 November 2019
• Accepted 1 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.075027

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Published by the American Physical Society