A Minimal Dark $SU(2)$ Origin of a Massless Dirac Neutrino

Abstract

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark $SU(2)_D$ gauge symmetry under which one right-handed-neutrino-like Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic $SU(2)_D$ doublet, while a discrete $Z_4$ symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector with a viable dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.