Improved sphaleron decoupling condition and the Higgs coupling constants in the real singlet-extended SM

TL;DR

This paper analyzes electroweak baryogenesis within the real singlet-extended SM by computing the sphaleron energy using a finite-temperature one-loop potential with daisy resummation. The authors derive an improved decoupling condition $\frac{v_C}{T_C} > (1.1-1.2)$, which tightens the viable parameter space for a strong first-order EWPT compared to the conventional criterion. They further connect this improved condition to deviations in Higgs couplings, showing that the triple-Higgs coupling $\lambda_{H_1H_1H_1}$ can deviate by up to about $16-50\%$ in representative regions, depending on the mixing and mass spectrum, with larger self-coupling shifts accompanying smaller gauge/fermion couplings. The results imply that HL-LHC/ILC measurements of Higgs properties could probe the EWPT dynamics in this class of models, while also highlighting theoretical uncertainties and the role of potential Landau-pole constraints in certain parameter choices. Overall, the work provides a more stringent link between early-universe phase transition dynamics and observable Higgs-sector signatures in extended scalar frameworks.

Abstract

We improve the sphaleron decoupling condition in the real singlet-extended standard model. The sphaleron energy is obtained using the finite temperature one-loop effective potential with daisy resummation. For moderate values of the model parameters, the sphaleron decoupling condition is found to be $v_C/T_C>(1.1-1.2)$, where $T_C$ denotes a critical temperature and $v_C$ is the corresponding vacuum expectation value of the doublet Higgs field at $T_C$. We also investigate the deviation of the triple Higgs boson coupling from its standard model value in the region where the improved sphaleron decoupling condition is satisfied. As a result of the improvement, the deviation of the triple Higgs boson coupling gets more enhanced. In a typical case, if the Higgs couplings to the gauge bosons/fermions deviate from the SM values by about 3 (10)%, the deviation of the triple Higgs boson coupling can be as large as about 16 (50)%, which is about 4 (8)% larger than that based on the conventional criterion $v_C/T_C>1$.

Figures (11)

• Figure 1: The shape of the tree-level potential $V_0(\varphi_H,\varphi_S)$ and $V^{Z_2}_0(\varphi_H,\varphi_S)$ as functions of $\varphi_H$ and $\varphi_S$ in left and right figures, respectively. In the left (right) figure, we take $m_{H_1}=125.5 \ {\rm GeV} ,m_{H_2}=150 \ (500) \ {\rm GeV}, v_S=100 \ (200) \ {\rm GeV}, \alpha=0^{\circ} \ (38^{\circ}), \mu_{S}^{\prime}=-30 \ (0) \ {\rm GeV}$, and $\mu_{HS}=-80 \ (0) \ {\rm GeV}$.
• Figure 2: The diverse patterns of the EWPT.
• Figure 3: The sphaleron energy (left panel) and $\lambda_{H,S,HS}$ (right panel) are plotted as a function of $\alpha$. We set $m_{H_1}=125.5$ GeV, $m_{H_2}=500$ GeV, $v_S=200$ GeV and $\mu_S=\mu^{\prime}_{S}=\mu_{HS}=$ 0 GeV.
• Figure 4: The possible region for the strong first-order phase transition in Case (i). In this figure, we set $m_{H_1}=125.5 \ {\rm GeV}$, $v_S=200 \ {\rm GeV}$, and $\mu_S^{\prime}=\mu_{HS}=\mu_S = 0$ GeV.
• Figure 5: The Higgs VEVs at $T_C$ (left panel), and $v_C/T_C$ and $\zeta_{\rm sph}$ (right panel) are presented as functions of $\alpha$ in Case (i).