Can Dirac neutrinos destabilize $\mathcal{Z}_2$ domain wall network?

TL;DR

This paper proposes a mechanism where Dirac neutrino masses induce explicit $ ext{Z}_2$ symmetry breaking radiatively, leading to domain wall decay and a gravitational wave signal, linking neutrino physics with cosmological observations.

Contribution

It introduces a novel connection between Dirac neutrino mass generation and domain wall destabilization via radiative effects, impacting gravitational wave predictions.

Findings

Radiative $ ext{Z}_2$ breaking scales inversely with the cube of the Dirac neutrino mass.

Gravitational wave spectrum scales with the sixth power of the Dirac neutrino mass.

Proposes that upcoming experiments can probe a wide range of Dirac seesaw scales.

Abstract

In particle physics model building, a discrete $\mathcal{Z}_2$ symmetry is often spontaneously broken for phenomenological reasons. When this breaking occurs dynamically in the early Universe, stable domain wall networks are formed, which can eventually dominate the cosmic energy density. To avoid this problem, explicit $\mathcal{Z}_2$-breaking terms in the scalar potential are usually introduced in an ad hoc manner. In this Letter, we show that if the same $\mathcal{Z}_2$ symmetry is also responsible for generating light Dirac neutrino masses, such explicit breaking terms can instead arise radiatively from the particles involved in the Dirac mass generation. We find that the resulting bias term scales inversely with the cube of the Dirac neutrino mass, leading to a gravitational wave spectrum proportional to the sixth power of the Dirac neutrino mass. This establishes a nontrivial connection between the Dirac seesaw scale, the domain wall annihilation epoch, and the resulting stochastic gravitational wave signal. We further demonstrate that a wide range of Dirac seesaw scales can be probed by upcoming gravitational wave and cosmic microwave background experiments, while part of the parameter space simultaneously explains the observed baryon asymmetry via Dirac leptogenesis.