Strongly Electroweak Phase Transition with U (1) L μ– L τ Gauged Nonzero Hypercharge Triplet

Abstract The extension of the Standard Model Higgs doublet with three nonzero hypercharge triplets is examineled in this article. The triplets are charged under additional $U(1)_{L_{\mu }-L_{\tau }}$ symmetry. We investigate the stability of the electroweak vacuum at both the tree level and the two-loop level. It is observed that the vacuum stability can be satisfied up to the Planck scale using two-loop $\beta$-functions. In contrast, due to the increase in the positive effect from triplet degrees of freedom, the perturbative unitarity can be satisfied only up to $10^{12}$ GeV. The parameter space allowed from the Planck scale stability is checked for the strongly electroweak first-order phase transition. The model satisfies the strongly first-order phase transition for the triplet bare mass parameters up to the TeV scale due to the sufficient contribution to the cubic term from the triplet degrees of freedom. It is observed that this model foresees a strongly first-order phase transition for all mass ranges until the degrees of freedom become heavy enough to decouple from the thermal bath. The benchmark points satisfying the strongly first-order phase transition are tested for gravitational-wave signatures. The benchmark points that are allowed from the Planck scale stability, strongly first-order phase transition also comes out to lie in the detectable frequency range of the LISA and BBO experiments.