# Scotogenic Dark Symmetry as a residual subgroup of Standard Model Symmetries

## TL;DR

This paper demonstrates how the scotogenic dark symmetry can emerge as a residual subgroup of the Standard Model's $U(1)_{B-L}$ symmetry, providing a unified framework for neutrino masses and dark matter stability.

## Contribution

It introduces a general framework where $U(1)_{B-L}$ is spontaneously broken to a residual $ ext{Z}_{2n}$ subgroup, linking neutrino Majorana nature and dark matter stability.

## Key findings

- Constructed models with dark matter as the neutrino loop particle
- Showed $U(1)_{B-L}$ can be gauged for richer phenomenology
- Provided conditions for residual symmetry to ensure neutrino and dark matter properties

## Abstract

We show that the scotogenic dark symmetry can be obtained as a residual subgroup of the global $U(1)_{B-L}$ symmetry already present in Standard Model. We propose a general framework where the $U(1)_{B-L}$ symmetry is spontaneously broken to an even $\mathcal{Z}_{2n}$ subgroup, setting the general conditions for neutrinos to be Majorana and the dark matter stability in terms of the residual $\mathcal{Z}_{2n}$. Under this general framework, as examples, we build a class of simple models where, in the scotogenic spirit, the dark matter candidate is the lightest particle running inside the neutrino mass loop. The global $U(1)_{B-L}$ symmetry in our framework being anomaly free can also be gauged in a straightforward manner leading to a richer phenomenology.