Electroweak phase transition with composite Higgs models: calculability, gravitational waves and collider searches

Abstract

We study the strong first order electroweak phase transition (SFOEWPT) with the SO(6)/SO(5) composite Higgs model, whose scalar sector contains one Higgs doublet and one real singlet. Six benchmark models are built with fermion embeddings in 1, 6, and 15 of SO(6). We show that SFOEWPT cannot be triggered under the minimal Higgs potential hypothesis, which assumes the scalar potential is dominated by the form factors from the lightest composite resonances. To get a SFOEWPT, the contributions from local operators induced by physics above the cutoff scale are needed. We take the 6 + 6 model as an example to investigate the gravitational waves prediction and the related collider phenomenology. arXiv:1909.02014v2 [hep-ph] 5 Dec 2019 6 Which has been proved to be gauge-independent in Refs. [53,54]. 7 We briefly comment on the other two possible SFOEWPT mechanisms. The first one is the "one-step"

Electroweak baryogenesis and gravitational waves in a composite Higgs model with high dimensional fermion representations

“…(2.9) are all expressed in terms of the momentum integrals of the form factors. Compared to the corresponding equations in the NMCHM with fermion embeddings in 15 or 6 [18], the λ η,hη here receive the leading order contribution from the α integrals and thus are enhanced. 2 For a QCD-like theory, the form factors can be explicitly written as a sum of the resonance poles…”

“…This is the so-called minimal Higgs potential hypothesis (MHP), which is generally adopted in the collider phenomenology studies of the CHMs [33][34][35][36][37][38]. In the aspect of cosmological implications, however, NMCHMs with fermion in 15 and lower representations cannot give a SFOEWPT under the MHP, due to the small quartic couplings in the potential [18]. In this section, we demonstrate that the 20 + 20 NMCHM is able to trigger a SFOEWPT, as the quartic coefficients are enhanced in the high-dimensional representation.…”

“…(2.11) the integrals are convergent, while the α and β integrals diverge quadratically and logarithmically, respectively. Inspired by the successful experience in QCD [43][44][45][46][47], people apply the Weinberg sum rules to the form factor integrals in CHMs to get a finite scalar potential [18,33,[35][36][37][38]. 3 We will also adopt this assumption here.…”

“…In this framework, the hierarchy problem is solved by identifying the Higgs doublet as the pseudo-Nambu-Goldstone bosons (pNGBs) from the spontaneous global symmetry breaking G/H of a new strong interacting sector [9][10][11]. In CHMs, the SFOEWPT can be triggered by the enlarged scalar sector, either from the dilaton of conformal invariance breaking [12,13] or from the extra pNGBs of G/H breaking [14][15][16][17][18]; and the new CP phase from the fermion sector can generate BAU [12][13][14][15][16][17].…”

“…As the fermion contribution is dominated by the top quark due to its large mass, hereafter we refer "fermion embedding" to the q L = (t L , b L ) T and t R embeddings. It has been shown that 6 and 15 representations are hard to trigger a SFOEWPT, mainly because of the smallness of the quartic couplings [17,18]. 1 The NMCHM with q L in 6 and t R in 20 has plenty of parameter space triggering the SFOEWPT since the 20 embedding can generate fairly large quartic couplings for the scalars [17].…”