Perturbativity Limits for Scalar Minimal Dark Matter with Yukawa Interactions: Septuplet

TL;DR

This paper investigates the perturbativity limits of scalar minimal dark matter models with a septuplet, showing that the Landau pole occurs at much lower scales than previously thought, but can be extended with Yukawa interactions and fine-tuning.

Contribution

It demonstrates that the perturbativity of scalar septuplet dark matter models is limited at around 10^8-10^9 GeV and proposes extensions with Yukawa interactions to raise this scale.

Findings

Landau pole at 10^8-10^9 GeV for 10 TeV septuplet

Yukawa interactions can extend the Landau pole to 10^14 GeV

Relaxing dark matter mass to 10^8 GeV can push the scale above the Planck scale

Abstract

The candidate of minimal dark matter (MDM) is limited if one demands perturbativity up to a very high scale, and it was believed that the MDM model with a real scalar septuplet could keep perturbative up to the Planck or GUT scale. In this work we point out that it is not true after taking into account the running of the quartic self-couplings of the scalar septuplet. For the septuplet mass around $10$ TeV, which is suggested by the observed dark matter relic abundance, these couplings would hit the Landau pole at a scale $\sim 10^8-10^9$ GeV, much lower than the Planck scale. We attempt to push up the Landau pole scale as high as possible by proposing an extension with extra Yukawa interactions of the septuplet. We find that in principle the Landau pole could be deferred to a scale of $\sim 10^{14}$ GeV if one could tolerate a serious fine-tuning of the initial condition of the Yukawa coupling. Moreover, if the MDM particle mass could be relaxed to $\sim10^8$ GeV, which would need some nonthermal production mechanisms to give a correct relic abundance, the Landau pole scale could be pushed up above the Planck scale.