# Dark matter stability and Dirac neutrinos using only Standard Model symmetries

## TL;DR

This paper introduces a framework where the spontaneous breaking of the Standard Model's $U(1)_{B-L}$ symmetry naturally results in stable dark matter and Dirac neutrinos, with potential for gauging.

## Contribution

It presents a novel mechanism linking dark matter stability and Dirac neutrino masses through residual symmetries from $U(1)_{B-L}$ breaking, compatible with Standard Model symmetries.

## Key findings

- Residual $ ext{Z}_n$ symmetry ensures dark matter stability
- Dirac neutrino masses generated at loop level
- Framework is anomaly free and gaugeable

## Abstract

We provide a generic framework to obtain stable dark matter along with naturally small Dirac neutrino masses generated at the loop level. This is achieved through the spontaneous breaking of the global $U(1)_{B-L}$ symmetry already present in Standard Model. The $U(1)_{B-L}$ symmetry is broken down to a residual even $\mathcal{Z}_n$; $n \geq 4$ subgroup. The residual $\mathcal{Z}_n$ symmetry simultaneously guarantees dark matter stability and protects the Dirac nature of neutrinos. The $U(1)_{B-L}$ symmetry in our setup is anomaly free and can also be gauged in a straightforward way. Finally, we present an explicit example using our framework to show the idea in action.