New Insights of Electroweak Phase Transition in NMSSM

We perform a detailed semi-analytical analysis of the electroweak phase transition (EWPT) property in NMSSM, which serves as a good benchmark model in which the 126 GeV Higgs mixes with a singlet. In this case, a strongly first order electroweak phase transition (SFOEWPT) is achieved by the tree-level effects and the phase transition strength ${\gamma }_c$ is determined by the vacua energy gap at $T=0$. We make an anatomy of the energy gap at both tree-level and loop-level and extract out a dimensionless phase transition parameter $R_{\kappa }\equiv 4\kappa v_s\mathrm{/}{A}_{\kappa }$, which can replace $A_{\kappa }$ in the parameterization and affect the light CP odd and even Higgs spectra. We find that SFOEWPT only occurs in $R_{\kappa }\sim -1$ and positive $R_\kappa \lesssim $\mathcal{O}$(10)$, which in the non-PQ limit case would prefer either a relatively light CP odd or CP even Higgs boson $\sim (60,100)$ GeV, therefore serves as a smoking gun signal and requires new search strategies at the LHC.