What is the criterion for a strong first order electroweak phase transition in singlet models?

Abstract

It is widely believed that the existence of singlet scalars in some Standard Model extensions can easily make the electroweak phase transition strongly first order, which is needed for the electroweak baryogenesis scenario. In this paper, we will examine the strength of the electroweak phase transition in the simplest extension of the Standard Model with a real singlet using the sphaleron energy at the critical temperature. We find that the phase transition is stronger by adding a singlet; and also that the criterion for a strong phase transition Ω(Tc)/Tc 1, where Ω = (υ 2 + (x − x0) 2 ) 1 2 and x (x0) is the singlet vev in the broken (symmetric) phase, is not valid for models containing singlets, even though often used in the literature. The usual condition υc/Tc 1 is more meaningful, and it is satisfied for a large part of the parameter space for physically allowed Higgs masses.

Probing triple-Higgs productions via4b2γdecay channel at a 100 TeV hadron collider

“…(λ 4 can be read out from the fit cross section given in Eq. (6).) In this case, the top mass effect is crucial and leads to a K-factor which is similar to the di-Higgs case.…”

“…One simple extension is adding a real scalar singlet to the SM Higgs sector [48][49][50][51][52]. Moreover, in this model, it is straightforward to produce a strong first order phase transition [6,7]. In particular, we find that there exists a part of parameter space where the quartic couplings play important roles.…”

Sphalerons and the electroweak phase transition in models with higher scalar representations

“…In figure 2, one can notice that the field profile f 0 (ξ) is just a deviation from unity similar to the singlet scalar profile in models with singlets [26] and it gets closer to unity as the X values becomes smaller and smaller. Indeed, it is exactly one for the representations (1, 0) and (2, 0) which means that in those cases the sphaleron energy is not affected by the existence of U(1) X gauge field.…”

“…It was shown in [26] that the kinetic term of the scalar field makes larger contribution to the sphaleron energy than the potential term. Therefore, for simplicity, we have considered CPinvariant scalar potential involving single scalar representation to determine the sphaleron solution.…”

“…the energy of the sphaleron [7]. Such baryon number violation induced by the sphaleron is one of the essential ingredients of Electroweak Baryogenesis [8][9][10][11][12][13] and therefore it has been extensively studied not only in the SM [14][15][16][17][18][19][20][21][22][23][24] and but also in extended SM variants such as, SM with a singlet [25,26], two Higgs doublet model [27], Minimal Supersymmetric Standard Model [28], the next-to-Minimal Supersymmetric Standard Model [29] and 5-dimensional model [30].…”