Minimal A4 Type-II Seesaw Realization of Testable Neutrino Mass Sum Rules

Abstract: We propose a flavour model based on an $A_4$ symmetry combined with a type-II seesaw mechanism for neutrino mass generation. The resulting neutrino mass matrix obeys a sum rule that, together with the measured mass-squared differences, fully determines the absolute neutrino mass spectrum. The constrained flavour structure yields correlated predictions for lepton mixing parameters, leads to inverted ordering after imposing mixing constraints, restricts the Majorana phases and implies a neutrinoless double beta decay rate close to its maximal value for inverted ordering. In the charged lepton sector an approximate triality symmetry arises in the seesaw limit, suppressing muon flavour-violating processes and allowing only specific $τ$ decay channels. The model provides a tightly constrained and experimentally testable framework linking neutrino masses, lepton mixing and lepton-number-violating observables.