Anomaly-free Abelian gauge symmetries with Dirac scotogenic models

TL;DR

This paper systematically explores anomaly-free Abelian gauge symmetries in standard model extensions to generate Dirac neutrino masses at one loop, identifying new solutions and conditions for consistent charge assignments.

Contribution

It provides a comprehensive scan for anomaly-free solutions with extra chiral fermions that enable scotogenic Dirac neutrino mass generation, considering various symmetry and operator dimensions.

Findings

Identified non-anomalous charge assignments for new fermions.

Classified solutions for active and dark U(1) symmetries.

Analyzed models with different operator dimensions and mediators.

Abstract

We perform a systematic analysis of standard model extensions with an additional anomaly-free gauge $U(1)$ symmetry, to generate Dirac neutrino masses at one loop. Under such symmetry, standard model fields could either transform or be invariant, corresponding to an active $U(1)_X$ or a dark $U(1)_D$ symmetry, respectively. Having an anomaly-free symmetry imposes nontrivial conditions to the number and charges of the unavoidable new states. We perform an intensive scan, looking for non-anomalous solutions for given number of extra chiral fermions. In particular, we concentrate on solutions giving rise to scotogenic neutrino masses via the effective Dirac mass operator. We study the cases where the Dirac mass operator with dimension 5 or 6, is mediated by Dirac or Majorana states, and corresponds to an active $U(1)_X$ or a dark $U(1)_D$ symmetry. Finally, we comment on the solutions featuring no massless chiral fermions.