Gravitational waves from phase transition in minimal SUSY U ( 1 ) B − L model

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)-(1000) TeV, it can generate stochastic gravitational waves in O(10)-O(100) Hz range if βn/Hn=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.