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

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 ${\beta }_{\mathrm{n}}/H_{\mathrm{n}}=1000$, 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.

Comments: 26 pages, 10 figures. Sensitivity curves of Advanced LIGO design, Cosmic Explorer and Einstein Telescope are overlaid on the plots of predicted gravitational wave spectrum. We have shown that the percolation of true-vacuum bubbles is completed in the benchmark with large supercooling where alpha_\theta(T_n)=1.5. References are added. Version accepted for publication in Physical Review D