Neutrino Mass in Left-Right Symmetry: From Majorana Signals to Dirac Predictions

Abstract

We review neutrino mass as a probe of restored parity in left-right symmetric theories, emphasizing the distinct Majorana and Dirac realizations. In the Majorana theory, lepton-number violation connects the seesaw mechanism to neutrinoless double beta decay, heavy-neutrino production and the Keung-Senjanovic process. The Dirac alternative removes these characteristic signals while retaining a relation between left- and right-handed flavor. The right-handed leptonic mixing matrix can then be reconstructed from low-energy data and the spontaneous parity-breaking parameter. Requiring the two lepton Yukawa matrices to admit a common real parity basis turns this reconstruction into a compatibility condition that determines the allowed Dirac phase on each branch. For three generations, this requirement reduces to a single rephasing-invariant CP-odd obstruction, which also governs the right-left modulus mismatch and the relative CP orientation. The small Dirac masses also restrict the parity deformation and its induced strong-CP phase. For compressed mixed-sign neutrino spectra, a tiny parity deformation can nevertheless generate large leptonic CP violation, despite stringent strong-CP constraints. The resulting branch-dependent correlations connect leptonic CP, the absolute neutrino mass and strong CP. We place this construction alongside radiative and unified approaches to predicting leptonic CP violation.