WIMP Dark Matter from a Natural Discrete Gauge Symmetry in the Standard Model

Abstract

The internal structure of the Standard Model implies a natural $\mathbb{Z}_4 \times \mathbb{Z}_3$ discrete gauge symmetry. Cancellation of the corresponding Dai--Freed anomalies requires the introduction of three right-handed neutrinos and three additional Majorana fermions $\chi_i$. This gauge symmetry forbids the decay of the lightest fermion $\chi_1$ into Standard Model particles, rendering it automatically stable and providing a dark matter candidate without introducing an ad hoc stabilizing symmetry and domain-wall problem. The mass of $\chi_1$ is generated by the vacuum expectation value of a singlet scalar near the electroweak scale, naturally realizing a weakly interacting massive particle (WIMP) freeze-out scenario. Dark matter annihilation proceeds through scalar mediation, allowing the observed relic abundance to be reproduced while remaining consistent with current direct-detection constraints. It naturally realizes the secluded dark matter scenario and can be further tested in the next generation of experiments.