Neutrino oscillation data and a pseudo-Dirac heavy neutral lepton

Abstract

Symmetry-protected seesaw models can accommodate light-neutrino oscillation data while keeping heavy neutral leptons (HNLs) within collider reach. In these models, the smallness of the light-neutrino masses is protected by an approximate lepton number (LN)-like symmetry that is broken only by small parameters. We study the minimal scenario in which the new states form one pseudo-Dirac HNL pair. The exact LN-conserving Dirac limit is diagonalised without expanding in the active-sterile mixing, and the small LN-violating entries are then included perturbatively. This yields a symmetry-protected flavour reconstruction of the active-heavy interaction matrix. The rank-two light-neutrino mass matrix fixes the normalised active-flavour direction, while the remaining high-energy information is a single complex light-heavy amplitude whose phase defines a CP-odd light-heavy invariant. For the normalised leading active-heavy interaction weights, this amplitude and the heavy-sector rotation cancel, leaving an ellipse in the flavour simplex determined by light-neutrino oscillation data and the Majorana phase. We also identify how the linear LN-violating terms enter coherent heavy-neutrino oscillations and the neutrinoless double beta effective mass.