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

TL;DR

This paper analyzes a classically conformal gauged B−L extension of the Standard Model, focusing on radiative B−L breaking that triggers electroweak symmetry breaking and yields a potentially observable gravitational wave signal. The authors examine the effective potential, including thermal corrections and QCD effects, and show that the QCD phase transition can influence the symmetry-breaking pattern in part of the parameter space. They perform a RG-based study of vacuum stability and perturbativity, finding regions where the EW vacuum is stabilized and the theory remains perturbative up to scales beyond the Planck scale, aided by gauge mixing. The phase transition is highly supercooled, leading to a thermal inflation epoch and a strong first-order transition that produces a GW spectrum with peak frequencies and amplitudes within the sensitivity of LISA for much of the parameter space. The results imply that LISA could probe substantial portions of this model’s parameter space, with Z′ collider signals providing complementary tests for model discrimination.

Abstract

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.

Figures (6)

• Figure 1: The evolution of $\lambda_H(t)$ as a function of the renormalization scale for $g_{{\rm B}-{\rm L}} = 0.1$, $m_{Z'} = 10^5$ GeV and three different values of $\tilde{g}$. All couplings have been set to the indicated values at the $w$ scale.
• Figure 2: Top panel:$M_{Z'} = 10$ TeV. Bottom panel:$\tilde{g} = -0.5$. In both the panels, coloured areas indicate the region of the parameter space where the stability of the symmetry-breaking vacuum is ensured up to the scale indicated in the legend. Below the dotted, dashed and solid lines we have the values of the parameters which allow the model to retain perturbativity of all the couplings (all couplings $< \sqrt{4\pi}$) beyond the Planck scale, at most up to the Planck scale and at most up to the GUT scale, respectively. Beyond the continuous black line, the model has a maximum perturbativity scale not exceeding the pure SM instability scale.
• Figure 3: The evolution of $S_3/T$ for a benchmark point with $m_{Z'} = 10\,{\rm TeV}$, $g_{{\rm B}-{\rm L}} = 0.26$, and $\tilde{g}(w) = -0.5$. The Majorana Yukawa couplings are assumed negligible.
• Figure 4: The bottom panel shows the behaviour of the characteristic temperatures relevant for the phase transition (defined in the text) as a function of the B--L coupling. The middle and top panels show, instead, the number of e-folds of thermal inflation and the average bubble separation (at $T=T_p$ in Hubble lengths), respectively. On the left of the vertical dotted line at $g_{{\rm B}-{\rm L}} \simeq 0.42$, the phase transition completes during the vacuum dominated era, whereas on the left of the vertical dotted line at $g_{{\rm B}-{\rm L}} \simeq 0.25$ the phase transition dynamics conclude after the QCD phase transition. Here $m_{Z'} = 10\,{\rm TeV}$, $\tilde{g}(w) = -0.5$, and the Majorana Yukawa couplings are assumed negligible.
• Figure 5: Gravitational wave spectrum for three benchmark points. Here $m_{Z'} = 10\,{\rm TeV}$, $\tilde{g}(w) = -0.5$ and the Majorana Yukawa couplings are assumed to be negligible.