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

Abstract

We improve the sphaleron decoupling condition in the real singlet-extended standard model (SM). 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 ${v}_{C}/{T}_{C}>(1.1\ensuremath{-}1.2)$, 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 ${v}_{C}/{T}_{C}>1$.