Strong electroweak phase transitions in the Standard Model with a singlet

Abstract

It is well known that the electroweak phase transition (EWPhT) in extensions of the Standard Model with one real scalar singlet can be first-order for realistic values of the Higgs mass. We revisit this scenario with the most general renormalizable scalar potential systematically identifying all regions in parameter space that develop, due to tree-level dynamics, a potential barrier at the critical temperature that is strong enough to avoid sphaleron wash-out of the baryon asymmetry. Such strong EWPhTs allow for a simple mean-field approximation and an analytic treatment of the free-energy that leads to very good theoretical control and understanding of the different mechanisms that can make the transition strong. We identify a new realization of such mechanism, based on a flat direction developing at the critical temperature, which could operate in other models. Finally, we discuss in detail some special cases of the model performing a numerical calculation of the one-loop free-energy that improves over the mean-field approximation and confirms the analytical expectations. One-loop Numerical AnalysisSo far, we have identified choices for the T = 0 parameters that lead to strong electroweak phase transitions in the mean-field approximation. It is straightforward to refine these results starting from the same tree-level parameters but including in the scalar potential one-loop T = 0 corrections and the full one-loop thermal integrals (which correctly take into account Boltzmann decoupling effects) further improved by daisy resummation. Details of this standard procedure are given in Appendix A. To illustrate the impact of this refinement, we show in Fig. 9 the ratio v c /T c in the mean-field approximation (blue dashed line) compared with

Non-resonant collider signatures of a singlet-driven electroweak phase transition

“…[29] in which the T = 0 singlet VEV is taken to be zero by appropriately shifting the singlet field (see also ref. [30]). We will also assume that h 2 is the mostly singlet-like state, with h 1 the Standard Model-like Higgs with m 1 = 125 GeV < m 2 .…”

“…The presence of additional singlet scalars with electroweak scale masses can give rise to a strong first order phase transition through a combination of different mechanisms [10,30]. A barrier at finite temperature between an electroweak-symmetric and -broken phase can be produced by new tree-level cubic terms in the scalar potential, by zero-temperature loop effects, or through significant thermal contributions.…”

“…refs. [10,30,55] for detailed discussions of the various possibilities in the high-temperature approximation).…”

Baryogenesis in the Zee-Babu model with arbitrary ξ gauge

“…[2,4,5] as well as its various extended versions [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For the SM, although the EWPT strength is larger than unity at the electroweak scale, the mass of the Higgs boson must be less than 125 GeV [2,4,5]; so the EWBG requires new physics beyond the SM at the weak scale [6].…”

Gravitational waves from the first order electroweak phase transition in the Z3 symmetric singlet scalar model

“…The mechanism to generate a thermal cubic term for h by a tree level barrier is most easily implemented in the extended Higgs sectors by a singlet S , containing effective tree-level cubic terms ∼ S 3 + S |H| 2 with H the SM Higgs doublet [5][6][7][8][9][10][11]. If the extended Higgs sector respects some symmetry such as Z 2 , under which S → −S and H → H, an alternative way to the desired tree level barrier is available in the symmetric limit where S does not acquire VEV at the present universe [7,[12][13][14][15][16]. Such a scenario is associated with multi-step PT's.…”