# Radiative Dirac Neutrino Mass with Dark Matter and it's implication to $0\nu 4\beta$ in the $U(1)_{B-L}$ extension of the Standard Model

## TL;DR

This paper proposes a $U(1)_{B-L}$ extended Standard Model with residual $Z_4$ symmetry that explains Dirac neutrino masses, stabilizes dark matter, and predicts an observable neutrinoless quadruple beta decay ($0
u 4eta$).

## Contribution

It introduces a novel anomaly-free $U(1)_{B-L}$ extension with residual $Z_4$ symmetry that links Dirac neutrino mass generation, dark matter stability, and predicts $0
u 4eta$ decay.

## Key findings

- Absence of neutrinoless double beta decay ($0
u 2eta$).
- Predicted enhancement of neutrinoless quadruple beta decay ($0
u 4eta$).
- Compatibility with dark matter detection and collider constraints.

## Abstract

The Standard Model gauge symmetry is extended by $U(1)_{B-L}$ which when spontaneously broken leads to residual $\mathbb{Z}_4$ symmetry. $U(1)_{B-L}$ gauge symmetry made anomaly free by introducing exotic SM singlets with corresponding $U(1)_{B-L}$ charges of $13$, $-14$, and $15$. $\mathbb{Z}_4$ symmetry ensures the Dirac nature of neutrinos, simultaneously stabilizing dark matter. Dirac neutrino mass is generated through scotogenic scenario. Dark matter, direct detection, cosmological constraints, and collider constraints analysis is performed. $\mathbb{Z}_4$ symmetry predicts the exact absence of neutrinoless double beta decay ($0\nu 2\beta$) and gives a prediction for an enhanced neutrinoless quadruple beta decay ($0\nu 4\beta$) via which this model can be tested. Model allows for Majorana dark matter as well as for long-lived dark matter candidates.