Archimedean Seesaw: Small Neutrino Masses and Large Lepton-number Violation

Abstract

Contrary to the common lore that observable lepton-number violation (LNV) is inevitably suppressed by tiny neutrino masses, we identify a class of seesaw models in which arbitrarily large LNV can naturally coexist with sub-eV neutrino masses. We construct a symmetry-protected texture-zero structure in the neutrino Yukawa couplings and heavy Majorana mass matrix that gives rise to the required accidental symmetry, thereby protecting the light neutrinos from acquiring mass even in the presence of arbitrarily large LNV in the heavy sector. Small neutrino masses arise naturally from lifting the texture-zero structure while preserving the underlying symmetry. The resulting framework offers a rich and experimentally accessible phenomenology, predicting Heavy Neutral Leptons with sizeable active-sterile mixing over a broad range of experimentally accessible masses, giving rise to observable LNV signatures at collider and intensity-frontier experiments.