New Insights of Electroweak Phase Transition in NMSSM

TL;DR

The paper investigates the electroweak phase transition in the NMSSM as a potential pathway to electroweak baryogenesis, employing a semi-analytical treatment of the zero- and finite-temperature Higgs potentials. It identifies a dimensionless parameter $R_κ=4 κ v_s / A_κ$ that governs singlet–doublet mixing and correlates with the vacua energy gap $ΔV$, determining the strength of the transition. The study finds that SFOEWPT occurs in regions with $R_κ\sim -1$ and modest positive values up to ${\cal O}(10)$, often predicting a smoking-gun signal in the form of a relatively light Higgs state (60–100 GeV) either CP-odd or CP-even, with distinct implications for Higgs phenomenology. These results tie EWPT viability to specific Higgs spectra, guiding future LHC searches and dark matter considerations in the NMSSM.

Abstract

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 $γ_c$ 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 $R_κ\equiv 4 κv_s / A_κ$, which can replace $A_κ$ in the parameterization and affect the light CP odd and even Higgs spectra. We find that SFOEWPT only occurs in $R_κ\sim -1$ and positive $R_κ\lesssim \mathcal{O}(10)$, 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.

Figures (15)

• Figure 1: Strong correlation between the strength of EWPT and the vacua energy gap $\Delta V$ at $T=0$. Left panel: $H_1-$ scenario; Right panel: $H_2-$ scenario. The vertical line stands for the $\Delta V = v^2 m_h^2 /4 = 1.18 \times 10^{8}$ GeV limit.
• Figure 2: $\Delta V_{\rm tree}$ and $\Delta V_{\rm num}$ (with loop corrections) versus $R_\kappa$. The left(right) two figures are the plots for the $H_1$($H_2$)$-$scenario. Clearly, the large negative energy gap at the tree-level $\Delta V_{\rm tree}$ is driven back to small positive value $\Delta V_{\rm num}$ through loop corrections.
• Figure 3: $R_{\kappa}$ versus $\gamma_{c}$ in Type-I transition, with color code denoting $\mu$. Left panel: $H_1-$scenario; Right panel: $H_2-$sceanrio.
• Figure 4: Loop-level gap $\Delta V_{\rm num}$ versus $\delta \equiv (u_s-v_s)/v_s$ for the Type-I transition for the $H_1-$ and $H_2-$scenario respectively.
• Figure 5: As in Fig. \ref{['T1_Rkap_PTS_mu']}, plots on the $\tan\beta-\gamma_{c}$ plane.