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Right-Handed Leptonic Mixing and Enhancement Bands in Left-Right Symmetry

Vladimir Tello

Abstract

Left-right (LR) symmetric theories predict right-handed charged currents whose flavor structure encodes the realization of parity. While the right-handed quark mixing matrix closely tracks its left-handed counterpart, the leptonic sector with purely Dirac neutrinos has remained structurally unclear. We show that, in contrast to the quark case, parity in the Dirac leptonic sector generically induces branch-dependent enhancement bands in which RH-LH misalignment becomes parametrically large despite small parity breaking. We derive analytic solutions of the LR consistency equation and demonstrate that the interplay between spontaneous parity violation and spectral near-degeneracies leads to a qualitatively new pattern of right-handed mixing. This establishes the Dirac leptonic sector of the minimal LR theory as a predictive and structurally distinct regime.

Right-Handed Leptonic Mixing and Enhancement Bands in Left-Right Symmetry

Abstract

Left-right (LR) symmetric theories predict right-handed charged currents whose flavor structure encodes the realization of parity. While the right-handed quark mixing matrix closely tracks its left-handed counterpart, the leptonic sector with purely Dirac neutrinos has remained structurally unclear. We show that, in contrast to the quark case, parity in the Dirac leptonic sector generically induces branch-dependent enhancement bands in which RH-LH misalignment becomes parametrically large despite small parity breaking. We derive analytic solutions of the LR consistency equation and demonstrate that the interplay between spontaneous parity violation and spectral near-degeneracies leads to a qualitatively new pattern of right-handed mixing. This establishes the Dirac leptonic sector of the minimal LR theory as a predictive and structurally distinct regime.
Paper Structure (12 sections, 16 equations, 2 figures)

This paper contains 12 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Minimal Dirac Left-Right setup
  3. Analytic Structure
  4. Small-$\epsilon$ regime.
  5. Quasi-degenerate regime.
  6. Parameter Space and Branch Structure
  7. Phenomenological constraints
  8. Direct neutrino-mass limits.
  9. Cosmological limits.
  10. Implications for strong CP.
  11. Collider implications.
  12. Conclusions

Figures (2)

  • Figure 1: Structure of the $(m_{\nu,\text{lightest}},\,\epsilon)$ plane in the minimal Dirac LR theory for normal (NH, left) and inverted (IH, right) hierarchies. The solid black curve shows the maximal $|\epsilon|$ for which Eq. \ref{['eq:master']} admits unitary solutions. The curves mark the locus $|\theta_{12}^R-\theta_{12}^L|=8^\circ$. The shaded band originates from mixed-sign branches in which the analytic denominators become parametrically large, producing localized RH--LH leptonic mixing misalignment. Vertical lines indicate the KATRIN and cosmological bounds on the lightest neutrino mass, while the horizontal line shows the constraint from the strong-CP phase $\bar{\theta}$.
  • Figure 2: Representative branch behavior of the solar-angle deviation $|\theta_{12}^R-\theta_{12}^L|$ as a function of $\epsilon=s_\alpha\tan2\beta$ for IH at $m_{\nu,\text{lightest}}=0.01\,\mathrm{eV}$. Gray curves show the mixed-sign branches for a fixed charged-lepton sign choice, while the black envelope indicates the extremal RH--LH deviations at fixed $\epsilon$. The vertical dashed line marks the $\bar{\theta}$ constraint. The shaded region lies beyond the corresponding bound.