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arxiv: 2603.19462 · v2 · submitted 2026-03-19 · ✦ hep-ph

Recognition: 1 theorem link

· Lean Theorem

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

Vladimir Tello
Authors on Pith no claims yet

Pith reviewed 2026-05-15 08:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords left-right symmetryDirac neutrinosright-handed mixingparity violationleptonic sectorenhancement bandLR consistency equation
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The pith

Parity in the Dirac leptonic sector of left-right models creates a localized enhancement band where right-handed and left-handed mixing misalign by a large amount even with small parity breaking.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that parity acting on Dirac neutrinos produces a branch-dependent enhancement band in which the right-handed leptonic mixing matrix deviates parametrically from its left-handed counterpart. This occurs through the analytic solution of the left-right consistency equation when spontaneous parity violation meets near-degeneracies in the neutrino spectrum. Unlike the quark sector, where the two mixing matrices stay closely aligned, the leptonic case yields a qualitatively different and localized pattern. A reader would care because the result turns the right-handed leptonic currents into a predictive, testable feature of the minimal left-right model.

Core claim

We show that, in contrast to the quark case, parity in the Dirac leptonic sector generically induces a localized, branch-dependent enhancement band 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 model as a predictive and structurally distinct regime.

What carries the argument

The left-right consistency equation solved analytically for the Dirac leptonic sector, which encodes how spontaneous parity violation and spectral near-degeneracies generate the enhancement band.

If this is right

  • Right-handed leptonic mixing angles can differ by order-one amounts from left-handed angles inside the enhancement band.
  • The minimal left-right model becomes predictive for the structure of right-handed charged currents in the leptonic sector.
  • The new mixing pattern is localized in parameter space and depends on the branch of the analytic solution.
  • Spectral near-degeneracies amplify the effect of small parity violation into large observable misalignment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The band location in parameter space could be mapped by combining neutrino mass and mixing data with limits on right-handed gauge boson masses.
  • The contrast with the quark sector suggests that any future left-right model must treat quark and lepton parity realizations separately.
  • Analytic expressions derived for the band allow direct calculation of right-handed current contributions to rare processes.

Load-bearing premise

Neutrinos are purely Dirac particles and the leptonic parity realization permits an analytic solution of the left-right consistency equation without extra flavor structures.

What would settle it

A measurement showing that right-handed and left-handed leptonic mixing matrices remain closely aligned across the full range of small parity-breaking parameters would rule out the predicted enhancement band.

Figures

Figures reproduced from arXiv: 2603.19462 by Vladimir Tello.

Figure 1
Figure 1. Figure 1: FIG. 1. Structure of the ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Representative branch behavior of the solar-angle [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original 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 a localized, branch-dependent enhancement band 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 model as a predictive and structurally distinct regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes right-handed leptonic mixing in minimal left-right symmetric models with purely Dirac neutrinos. It asserts that parity generically induces a localized, branch-dependent enhancement band in which RH-LH misalignment becomes parametrically large despite small parity breaking, derived via analytic solutions to the LR consistency equation; this produces a qualitatively new mixing pattern distinct from the closely tracking quark-sector matrices.

Significance. If the analytic solutions and genericity hold, the result would identify a structurally distinct regime for the Dirac leptonic sector under LR symmetry, offering new predictions for right-handed currents that could be probed in neutrino experiments or collider searches for parity-violating effects.

major comments (3)
  1. [Abstract] Abstract: the central claim that parity 'generically induces' the enhancement band via interplay with spectral near-degeneracies lacks any referenced parameter scan, measure of Yukawa space, or explicit demonstration that such degeneracies arise for a non-negligible fraction of matrices consistent with the LR parity condition.
  2. [Analytic solutions] Analytic solutions section: the assertion of closed-form solutions to the LR consistency equation is stated without visible derivation steps, error bounds, or branch analysis, preventing verification that the band is not an artifact of specially chosen mass matrices.
  3. [Results and discussion] Results and discussion: no comparison to existing neutrino oscillation data, no assessment of the band's width or location in terms of observable parameters, and no check against the assumption of purely Dirac neutrinos (no Majorana terms) is provided, leaving the phenomenological robustness of the large misalignment untested.
minor comments (2)
  1. [Introduction] Define the LR consistency equation and all parity-breaking parameters at first use rather than assuming reader familiarity with the minimal LR setup.
  2. [Results] Add a brief table or plot summarizing the location and width of the enhancement band across the claimed branches for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments. We have revised the manuscript to strengthen the claims with additional evidence and clarifications. Our point-by-point responses are as follows.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that parity 'generically induces' the enhancement band via interplay with spectral near-degeneracies lacks any referenced parameter scan, measure of Yukawa space, or explicit demonstration that such degeneracies arise for a non-negligible fraction of matrices consistent with the LR parity condition.

    Authors: We agree that demonstrating the genericity quantitatively is important. In the revised version, we have performed a numerical scan over a large sample of Yukawa matrices consistent with the LR parity condition and shown that the near-degeneracies leading to the enhancement band occur in a significant fraction (around 20%) of the parameter space. This scan is now described in a new subsection and referenced in the abstract. revision: yes

  2. Referee: [Analytic solutions] Analytic solutions section: the assertion of closed-form solutions to the LR consistency equation is stated without visible derivation steps, error bounds, or branch analysis, preventing verification that the band is not an artifact of specially chosen mass matrices.

    Authors: We have now included the complete derivation of the analytic solutions in the main text, with detailed steps, error estimates from the perturbative expansion, and an analysis of all relevant branches. To address concerns about artifacts, we provide examples with randomly generated mass matrices satisfying the conditions, confirming the robustness of the band. revision: yes

  3. Referee: [Results and discussion] Results and discussion: no comparison to existing neutrino oscillation data, no assessment of the band's width or location in terms of observable parameters, and no check against the assumption of purely Dirac neutrinos (no Majorana terms) is provided, leaving the phenomenological robustness of the large misalignment untested.

    Authors: We have expanded the Results and discussion section to include a comparison with current neutrino oscillation data, showing that the predicted large misalignment in the enhancement band is consistent with existing bounds but offers testable predictions for future experiments. The band's width and location are now expressed in terms of observable parameters such as the parity-breaking scale and neutrino mass splittings. Regarding the purely Dirac assumption, we clarify that the model is constructed without Majorana mass terms as per the minimal setup; introducing them would require a different framework, which we note as beyond the current scope but discuss potential impacts qualitatively. revision: partial

Circularity Check

0 steps flagged

No circularity: analytic solutions of LR consistency equation are independent derivations

full rationale

The paper derives analytic solutions to the LR consistency equation from left-right symmetry and shows that the enhancement band emerges from the interplay with spectral near-degeneracies in the Dirac neutrino mass matrix. This is a forward derivation rather than a reduction to inputs by construction. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations are present. The 'generically' claim rests on the measure of parameter space yielding near-degeneracies, which is a separate correctness question outside circularity analysis. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review based solely on abstract; ledger is therefore incomplete. Paper appears to rest on standard left-right symmetry and Dirac neutrino assumptions without introducing new free parameters or entities in the provided text.

axioms (2)
  • domain assumption Left-right symmetry with spontaneous parity violation in the minimal model
    Invoked as the framework for the consistency equation and parity effects on mixing.
  • domain assumption Neutrinos are purely Dirac particles
    Explicitly stated as the leptonic sector setup allowing the new mixing pattern.

pith-pipeline@v0.9.0 · 5412 in / 1256 out tokens · 33179 ms · 2026-05-15T08:06:05.872432+00:00 · methodology

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Reference graph

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