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

TL;DR

This paper refines the sphaleron decoupling condition in the real singlet-extended Standard Model, showing that the condition is slightly more relaxed and that deviations in Higgs couplings can significantly enhance the triple Higgs coupling deviation.

Contribution

It provides an improved sphaleron decoupling criterion and explores its impact on Higgs coupling deviations in the extended Standard Model.

Findings

Sphaleron decoupling condition is $v_C/T_C > 1.1-1.2$ for moderate parameters.

Deviations in Higgs couplings can increase the triple Higgs coupling deviation up to 50%.

The improved criterion results in a 4-8% larger deviation of the triple Higgs coupling compared to the conventional criterion.

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 $v_C/T_C>1$.