Freeze-in Production of Pseudo-Nambu-Goldstone Dark Matter Model with a Real Scalar

TL;DR

This paper explores a pseudo-Nambu-Goldstone boson dark matter model with a real scalar, produced via freeze-in, ensuring correct relic abundance and vacuum stability up to the Planck scale through renormalization group analysis.

Contribution

It introduces a high-energy scalar extension to stabilize the electroweak vacuum and constrains model couplings using renormalization group equations and stability conditions.

Findings

The model reproduces observed dark matter relic abundance.

Couplings are tightly constrained by vacuum stability and perturbativity.

Relic abundance is largely insensitive to scalar couplings unless specific production channels dominate.

Abstract

In this work, we study a pseudo-Nambu-Goldstone boson (pNGB) dark matter model extended with a real scalar. The dark sector is assumed to be feebly coupled with the standard model (SM) via a Higgs portal, so that the pNGB dark matter is produced by the freeze-in mechanism. Since the production happened in a very high energy era, we introduce an extra scalar field which is weakly coupled to the SM for stablizing the electroweak vacuum. Our model can reproduce the correct relic abundance of dark matter favored by observations. In addition, we determine the evolution of couplings in higher energy scale by solving the renormalization group equations, and show that the self coupling of the real scalar, $\lambda_S$, and the mixing coupling between the Higgs field and the real scalar, $\lambda_{HS}$ are stringently constrained by the conditions of vacuum stability and couplings perturbativity up to the Planck scale. We also find that the relic abundance of DM is insensitive to the values of $\lambda_S$ and $\lambda_{HS}$ unless the dominant production processes are $\overline{H}+H(S+S)\to\phi+\phi$ via t- and u-channels.