Phase transition and vacuum stability in the classically conformal B-L model

Within classically conformal models, the spontaneous breaking of scale invariance is usually associated to a strong first order phase transition that results in a gravitational wave background within the reach of future space-based interferometers. In this paper we study the case of the classically conformal gauged B-L model, analysing the impact of this minimal extension of the Standard Model on the dynamics of the electroweak symmetry breaking and derive its gravitational wave signature. Particular attention is paid to the problem of vacuum stability and to the role of the QCD phase transition, which we prove responsible for concluding the symmetry breaking transition in part of the considered parameter space. Finally, we calculate the gravitational wave signal emitted in the process, finding that a large part of the parameter space of the model can be probed by LISA.