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

Abstract

We consider an extension to the Standard Model (SM) with two extra real singlet scalars which both interact with the Higgs particle in the SM and one of the scalars 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. It is shown 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 Λ Pl . Therefore, the presence of the extra scalars not only reduce the fine-tuning problem of the Higgs mass to a given scale Λ ≪ Λ Pl , but also the singlet scalars do not receive large corrections up to the scale Λ. For the case of two-scalar DM model we find Λ = 10 8 GeV.