Lattice investigation of custodial two-Higgs-doublet model at weak quartic couplings

TL;DR

This study non-perturbatively investigates a custodial two-Higgs-doublet model on the lattice, exploring spontaneous symmetry breaking, scalar spectrum, gauge coupling behavior, and finite temperature electroweak transition at weak quartic couplings.

Contribution

It provides the first non-perturbative lattice analysis of the custodial two-Higgs-doublet model, including symmetry breaking, spectrum, and phase transition properties.

Findings

Spontaneous custodial symmetry breaking occurs in certain parameter regions.

Additional scalar masses can be below the W boson mass at weak couplings.

The electroweak transition exhibits a smooth crossover behavior.

Abstract

The $SU(2){-}$gauged custodial two-Higgs-doublet model, which shares the same global-symmetry properties with the standard model, is studied non-perturbatively on the lattice. The additional Higgs doublet enlarges the scalar spectrum and opens the possibility for spontaneous breaking of the global symmetry. In this work we start by showing the occurrence of spontaneous breaking of the custodial symmetry in a region of the parameter space of the model. Following this, both the spectrum and the running of the gauge coupling are examined at weak quartic couplings in the presence of the custodial symmetry. The calculations are performed with energy cutoffs ranging from 300 to 600 GeV on a line of constant standard model physics, obtained by tuning bare couplings to fix the ratio between the masses of the Higgs and the $W$ bosons, as well as the value of the renormalized gauge coupling at the scale of the $W$ boson mass. The realizable masses for the additional scalar states are explored. For the choice of bare quartic couplings in this work, the estimated lower bound of these masses is found to be well below the $W$ boson mass, and independent of the cutoff. We also study the finite temperature electroweak transition along this line of constant standard model physics, revealing properties of a smooth crossover behavior.