Confronting the real scalar septuplet minimal dark matter model with vacuum stability, perturbativity, and Type-I and Type-III seesaws

TL;DR

This paper investigates a real scalar septuplet dark matter model, analyzing its relic abundance, vacuum stability, and perturbativity constraints, especially when combined with Type-I and Type-III seesaw mechanisms, across various energy scales.

Contribution

It provides a comprehensive analysis of the scalar septuplet dark matter model, including effects of seesaw mechanisms on vacuum stability and perturbativity up to the Planck scale.

Findings

Dark matter mass is constrained to be above 8.8 TeV without Sommerfeld effect and above 25 TeV with it.

Vacuum stability and perturbativity impose narrow parameter regions for quartic couplings.

Seesaw scales significantly affect the allowed parameter space, especially in Type-I and Type-III scenarios.

Abstract

We study a real scalar septuplet model which has a neutral component regarded as a dark matter particle candidate. The calculation of its thermal relic abundance without (with) the Sommerfeld effect suggests that the observed value corresponds to the mass of the dark matter particle $m_0 \gtrsim 8.8~(25)~\mathrm{TeV}$. Two extra quartic couplings $\lambda_2$ and $\lambda_3$ introduced in this model affect the running of other couplings, and hence the vacuum stability and the perturbativity up to the Planck scale. Therefore, the vacuum stability and the perturbativity conditions can constrain these couplings into a narrow region in the $\lambda_2$-$\lambda_3$ plane. Other constraints from $h\to\gamma\gamma$, electroweak oblique parameters, and direct and indirect DM searches are also investigated. Moreover, we survey the vacuum stability and the perturbativity in the model combining the septuplet with the Type-I or Type-III seesaw. The running of couplings is further altered when the energy scale goes above the seesaw scale. In the Type-I case, when the seesaw scale $\sim 10^{15}~\mathrm{GeV}$, the vacuum stability condition makes the acceptable region in the $\lambda_2$-$\lambda_3$ plane much narrower. In the Type-III case, if the seesaw scale is $\lesssim 52~\mathrm{TeV}$ or $\gtrsim 10^{15}~\mathrm{GeV}$, the acceptable region vanishes.