The hierarchy problem and the vacuum stability in two-scalar dark matter model

TL;DR

This paper explores a two-scalar extension of the Standard Model that addresses dark matter relic abundance, evades detection bounds, and alleviates the hierarchy problem by satisfying Veltman conditions at accessible energy scales.

Contribution

It introduces a two-scalar dark matter model that simultaneously explains relic abundance, maintains vacuum stability, and reduces fine-tuning of the Higgs mass through Veltman condition satisfaction.

Findings

Model explains dark matter relic abundance.

Evades direct detection constraints.

Satisfies Veltman conditions at 300 GeV and 1 TeV.

Abstract

We consider an extension to the Standard Model (SM) with two extra real singlet scalars which interact with the SM Higgs particle. The lighter scalar is taken as the dark matter (DM) candidate. We show that the model successfully explains the relic abundance of the DM in the universe and evades the strong bounds from direct detection experiments while respecting the perturbativity and the vacuum stability conditions. In addition, we study the hierarchy problem within the Veltman approach by solving the renormalization group equations at one-loop. We demonstrate that the addition of the real singlet scalars contributes to the Veltman parameters which in turn results in satisfying the Veltman conditions much lower than the Planck scale $ \Lambda_\text{Pl}$ down to the electroweak scale. Therefore, the presence of the extra scalars solves the fine-tuning problem of the Higgs mass. For the case of the two-scalar DM model we find two representative points in the viable parameter space which satisfy also the Veltman conditions at $\Lambda = 300$ GeV and $\Lambda = 1$ TeV.