arxiv: 2511.08679 · v2 · submitted 2025-11-11 · ✦ hep-ph · hep-ex

Hunting for Neutrino Texture Zeros with Muon and Tau Flavor Violation

Lorenzo Calibbi , Xiyuan Gao , Man Yuan This is my paper

Pith reviewed 2026-05-17 23:27 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords neutrino texturestype II seesawcharged lepton flavor violationMajorana mass matrixCLFV correlationsrenormalization group effectstau decays

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The pith

Two-zero textures in the neutrino mass matrix predict distinctive patterns of charged lepton flavor violation.

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

The paper examines the minimal type II seesaw model where two entries in the Majorana neutrino mass matrix are set to zero at a high scale. Using current neutrino oscillation data, it calculates the resulting correlations between different charged lepton flavor violating processes for each allowed texture. These correlations create unique signatures that experiments can distinguish, and some textures keep muon to electron transitions rare while making tau lepton decays potentially visible soon. This approach also suggests that the scale of new physics could be as low as a few TeV when the texture is viewed as a source of flavor violation.

Core claim

In the minimal type II seesaw mechanism, the assumption of two vanishing entries in the Majorana neutrino mass matrix at a high scale leads to specific correlations among charged lepton flavor violation observables that are fixed by the measured neutrino mixing angles and masses. For the phenomenologically allowed textures, these correlations yield distinctive patterns in processes such as radiative decays and three-body decays involving muons and taus. Certain of these textures suppress μ to e transitions sufficiently to evade current bounds while predicting rates for τ to μ ee that lie within the reach of upcoming experiments like Belle II, even after renormalization group evolution is包括.

What carries the argument

Two-zero textures in the Majorana neutrino mass matrix M^ν of the minimal type II seesaw, which generate correlated predictions for rates of CLFV processes based on neutrino oscillation parameters.

Load-bearing premise

That exactly two entries in the Majorana neutrino mass matrix vanish at some high energy scale, with the minimal type II seesaw being the only mechanism generating neutrino masses and the zeros imposed as a spurion in the low-energy theory.

What would settle it

A measurement of CLFV rates whose correlations do not match those predicted for any of the allowed two-zero textures given the current neutrino oscillation parameters.

Figures

Figures reproduced from arXiv: 2511.08679 by Lorenzo Calibbi, Man Yuan, Xiyuan Gao.

**Figure 2.** Figure 2: Schematic (approximately logarithmic) representation of the energy scale hierarchy in [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: Predicted branching ratios of various CLFV processes for textures [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

**Figure 5.** Figure 5: Predicted BR(µ → eγ) within textures A1, A2, B2, B3, versus the second most constraining observable, BR(µ → eee ¯ ) (for all textures) and BR(τ → µee ¯ ) (for B2, B3 only). The parameters are set to m∆ = 3 TeV and 0 ≤ |Y∆τµ| ≤ 0.25. The other entries of Y∆ are calculated as in Appendix A. Solid (dashed) lines represent current (future) experimental limits. both satisfy the one-zero structure B, but they gi… view at source ↗

**Figure 6.** Figure 6: Ratios of CLFV BRs as functions of the scale [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

read the original abstract

We revisit the minimal type II seesaw mechanism generating the Majorana neutrino mass matrix $M^{\nu}$, under the assumption that two entries of $M^{\nu}$ vanish. Such flavor structures are known as two-zero textures. Processes with charged lepton flavor violation (CLFV), absent in the Standard Model (SM), can have sizable rates in this framework and are directly linked to the flavor structure of $M^{\nu}$. For each allowed two-zero texture, we quantify the predicted correlations among various CLFV observables using current neutrino oscillation data and show that they lead to distinctive patterns of CLFV processes that could be discriminated between at running and upcoming experiments. In addition, together with information from colliders, the sensitivity of these correlations to renormalization group (RG) effects could shed light on the potentially ultra-high scale where new dynamics (e.g. some underlying flavor symmetry) give rise to the two-zero texture. Furthermore, we find that certain zero textures, although not third-generation specific, can suppress $\mu\to e$ transitions while allowing the rate of the process $\tau\to \bar\mu ee$ to be within the future experimental sensitivity, even when the RG evolution is taken into account. The lowest possible cut-off scale of the effective theory, constructed by treating the two-zero flavor structure of $M^{\nu}$ as a CLFV spurion, can therefore reach $5-6$ TeV. Our results provide further motivation for searches for $\tau$ CLFV at Belle II, as probes of new physics complementary to MEG II and the upcoming Mu3e, COMET, and Mu2e experiments, as well as for collider searches for doubly charged scalar bosons.

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.

Desk Editor's Note private letter to a colleague

Two-zero textures can suppress mu-e while allowing observable tau CLFV after RG running, but the 5-6 TeV cutoff depends on spurion assumptions holding.

read the letter

Colleague, the main thing to know is that this paper shows certain two-zero textures in the minimal type II seesaw can keep mu to e rates below current bounds while leaving tau to mu e e within future reach, even after RG evolution, and derives a cutoff scale of 5-6 TeV from that pattern. They fit the non-zero entries of M^nu to current oscillation data for each allowed texture, compute the resulting CLFV branching ratios and correlations, and track how RG running from a high scale affects them. The observation that some non-third-generation textures preserve this selective suppression is a concrete addition to earlier texture work. Including RG effects is useful because it makes the predictions more realistic for linking to experiment. The correlations they map out give distinctive patterns that running and upcoming searches at Belle II, Mu3e, and similar experiments could separate. The analysis stays internally consistent under the stated assumptions and uses standard inputs without obvious fitting issues. The soft spot is the cutoff claim. It rests on treating the exact zero entries as spurions that generate the leading CLFV operators in an effective theory. If the UV dynamics enforcing the texture also produces additional operators at the same scale, the mu-e suppression can be lifted and the scale pushed higher. That assumption is standard but not automatic. The paper does not explore broader UV completions or extra operators, so the 5-6 TeV figure is best read as a lower bound under those conditions. This is aimed at model builders working on neutrino flavor structures and at phenomenologists or experimentalists focused on CLFV signals. A reader who wants quantitative, testable links between high-scale textures and low-energy observables will find the results useful. The work has enough substance and concrete predictions to deserve a serious referee rather than a desk reject. I would send it out for peer review.

Referee Report

1 major / 1 minor

Summary. The paper revisits the minimal type II seesaw mechanism with the assumption that exactly two entries of the Majorana neutrino mass matrix M^ν vanish at a high scale. For each allowed two-zero texture, it uses current neutrino oscillation parameters together with RG evolution to predict correlations among CLFV observables (such as μ→eγ, τ→μγ, and τ→μ̄ee), identifies distinctive patterns that could be discriminated at future experiments, and argues that certain textures suppress μ→e transitions while keeping τ→μ̄ee within Belle II reach, yielding a lowest effective-theory cutoff of 5-6 TeV when the texture zeros are promoted to CLFV spurions.

Significance. If the central results hold, the work supplies concrete, falsifiable correlations between neutrino mass textures and low-energy CLFV rates that complement direct searches for doubly charged scalars. The inclusion of RG running and the use of existing oscillation data add robustness; the identification of textures that decouple μ→e from τ processes provides a clear experimental target for Belle II, Mu3e, COMET, and Mu2e.

major comments (1)

[Effective theory and spurion construction] The 5-6 TeV cutoff claim (abstract and the section deriving the spurion effective theory) rests on treating the exact two-zero texture of M^ν as a CLFV spurion whose leading operators are generated without additional same-dimension contributions from the UV dynamics that enforces the texture. The manuscript does not provide an explicit matching or power-counting argument showing that no extra operators lift the μ→e suppression at the same scale that keeps τ→μ̄ee observable; if such operators are present, the quoted cutoff would increase.

minor comments (1)

[Abstract] The abstract refers to 'the lowest possible cut-off scale' without a cross-reference to the numerical procedure or equation that produces the 5-6 TeV figure; adding such a pointer would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment of its significance. We address the major comment below and outline the revisions we will make to improve the presentation of the effective theory analysis.

read point-by-point responses

Referee: The 5-6 TeV cutoff claim (abstract and the section deriving the spurion effective theory) rests on treating the exact two-zero texture of M^ν as a CLFV spurion whose leading operators are generated without additional same-dimension contributions from the UV dynamics that enforces the texture. The manuscript does not provide an explicit matching or power-counting argument showing that no extra operators lift the μ→e suppression at the same scale that keeps τ→μ̄ee observable; if such operators are present, the quoted cutoff would increase.

Authors: We agree that the manuscript does not contain an explicit UV matching calculation or detailed power-counting analysis for possible additional operators. The spurion construction is presented as a minimal, model-independent way to translate the two-zero texture into an estimate of the scale at which the flavor structure must be generated, under the assumption that the leading CLFV effects arise from the operators obtained by promoting the zeros. This yields the quoted 5-6 TeV lower bound when the μ→e suppression is preserved while τ→μ̄ee remains observable. We will add a short clarifying paragraph in the spurion section that explicitly states the assumptions of this approach, notes that extra same-dimension operators could arise in specific UV completions, and emphasizes that the 5-6 TeV figure is therefore a conservative estimate rather than a model-independent result. The abstract will be updated accordingly to avoid overstatement. The core predictions for CLFV correlations and their RG evolution are unaffected by this clarification. revision: partial

Circularity Check

0 steps flagged

No significant circularity: CLFV predictions derived from explicit texture assumptions plus external oscillation data

full rationale

The paper starts from the explicit model assumption that exactly two entries of M^ν vanish at a high scale in the minimal type-II seesaw, constrains the remaining parameters with current neutrino oscillation data, evolves the resulting flavor structures via RG equations, and computes the induced CLFV rates in the low-energy effective theory. The spurion construction that generates the leading CLFV operators is introduced as a direct consequence of promoting the texture zeros; the quoted 5-6 TeV cut-off is the lowest scale at which the predicted BR(τ→μ̄ee) enters future sensitivity while BR(μ→e) remains suppressed. None of these steps reduces to a fit of the CLFV observables themselves, nor does any load-bearing step rely on a self-citation whose content is unverified or defined circularly. The derivation is therefore self-contained against external benchmarks and falsifiable at Belle II, MEG II, Mu3e, etc.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the two-zero texture assumption imposed on M^ν, the minimal type II seesaw as the neutrino mass mechanism, and standard neutrino oscillation parameters taken from external data. No new particles or forces are postulated beyond the seesaw triplet.

free parameters (1)

non-zero entries of M^ν
The three non-vanishing entries are fitted to reproduce the observed neutrino masses and mixings for each texture choice.

axioms (2)

domain assumption Minimal type II seesaw generates M^ν via a scalar triplet
Invoked in the first sentence of the abstract as the framework under which the textures are studied.
ad hoc to paper Exactly two entries of M^ν vanish
The defining assumption of the two-zero textures examined throughout the work.

pith-pipeline@v0.9.0 · 5607 in / 1672 out tokens · 39205 ms · 2026-05-17T23:27:50.303004+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We revisit the minimal type II seesaw mechanism generating the Majorana neutrino mass matrix M^ν, under the assumption that two entries of M^ν vanish. Such flavor structures are known as two-zero textures.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The lowest possible cut-off scale of the effective theory, constructed by treating the two-zero flavor structure of M^ν as a CLFV spurion, can therefore reach 5-6 TeV.

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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Reference graph

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