High-scale validity of a model with Three-Higgs-doublets

TL;DR

This paper investigates the high-scale validity of a three-Higgs-doublet model with S3 symmetry, analyzing vacuum stability, perturbativity, and dark matter implications, finding one scenario valid up to the Planck scale.

Contribution

It provides a detailed analysis of the high-energy behavior of a three-Higgs-doublet model with S3 symmetry, identifying conditions for vacuum stability and dark matter viability.

Findings

The scenario with three nonzero vevs is invalid beyond 10^7 GeV.

The scenario with one nonzero vev remains valid up to the Planck scale.

The model can successfully account for cold dark matter phenomenology.

Abstract

We consider a three-Higgs doublet scenario in this paper, invariant under the discrete group S3 , and probe its high-scale validity by allowing the model parameters to evolve under a renormalization group. We choose two particular alignments of vacuum expectation values (vev) for our study, out of a set of several such possible ones. All three doublets receive nonzero vacuum expectation values in the first case, and in the second case, two of the doublets remain without vev. The constraints on the parameter space at low energy, including the measured value of the Higgs mass and the signal strengths, oblique corrections and also measurements of relic density and direct detection rates are juxtaposed with the conditions of vacuum stability, perturbativity and unitarity at various scales. We find that the scenario with three nonzero vevs is not valid beyond 107 GeV, assuming no additional physics participates at the intermediate scales. On the contrary, the scenario with only one nonzero vev turns out to be a successful model for cold dark matter phenomenology, which also turns out to be valid up to the Planck scale at the same time. Stringent restrictions are obtained on the model parameter space in each case. Thus, the S3 symmetric scalar sector emerges as an ultraviolet complete theory.