arxiv: 2601.18237 · v3 · submitted 2026-01-26 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Revisiting μ-e conversion in R-parity violating SUSY

Yu-Qi Xiao , Xiao-Gang He , Hong-Yi Niu , Rong-Rong Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:08 UTC · model grok-4.3

classification ✦ hep-ph

keywords μ-e conversionR-parity violationlepton flavor violationrenormalization group runningsupersymmetrytrilinear couplingsLFV constraints

0 comments

The pith

Renormalization group running strengthens limits on R-parity violating couplings in μ-e conversion by up to 80 percent.

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

This paper recalculates bounds on lepton flavor violation in supersymmetric models with R-parity violation by evolving the trilinear couplings via renormalization group equations from a high scale down to the weak scale. It extracts updated upper limits on fifteen combinations of the λ′ couplings and six combinations of the λ couplings by confronting them with existing data on μ-e conversion, μ→eγ, and μ→eee. Running effects shift most limits by less than thirty percent but tighten some by roughly eighty percent, an adjustment that cannot be ignored. Upcoming experiments COMET and Mu2e are projected to deliver tighter and more complete coverage of these couplings than the decay channels alone.

Core claim

Including renormalization group running of the trilinear R-parity violating couplings modifies the derived upper limits on the fifteen λ′ and six λ combinations, with improvements reaching ∼80% in selected cases, while μ-e conversion measurements are shown to constrain most combinations more comprehensively than μ→eγ or μ→eee data.

What carries the argument

Renormalization group evolution of the trilinear R-parity violating λ and λ′ couplings that generate low-energy lepton flavor violation.

If this is right

Upper limits on specific λ′ and λ combinations tighten by up to 80% once running is included.
COMET and Mu2e will set stricter bounds on most trilinear combinations than current μ→eγ and μ→3e experiments.
RG effects must be retained for accurate extraction of coupling limits from LFV data.
Several previously underexplored coupling combinations now receive quantitative bounds.

Where Pith is reading between the lines

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

Refined limits may narrow the parameter space in which R-parity violation generates neutrino masses.
Similar running corrections are likely relevant for other LFV processes in the same models.
High-scale SUSY constructions must match onto low-energy LFV observables after running.
Precision future data could help distinguish the ultraviolet origin of the violating couplings.

Load-bearing premise

Trilinear R-parity violating interactions are assumed to dominate lepton flavor violation and their renormalization group evolution is taken to be reliable without large higher-order corrections or interference from other sectors.

What would settle it

A measured μ-e conversion rate lying between the no-running and RG-improved predictions, or violating the RG-improved limit while satisfying the fixed-scale limit, would test whether the running effects must be included.

Figures

Figures reproduced from arXiv: 2601.18237 by Hong-Yi Niu, Rong-Rong Zhang, Xiao-Gang He, Yu-Qi Xiao.

**Figure 2.** Figure 2: FIG. 2. The upper limits with and without RG effects on the combinations of [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗

read the original abstract

The $\mu$-$e$ conversion process is one of the most powerful ways to test lepton-flavor-violating (LFV) interactions involving charged leptons. The standard model with massive neutrinos predicts an extremely low rate for $\mu$-$e$ conversion, making this process an excellent probe for testing LFV arising from new physics. Among many theoretical models that can induce LFV, the Supersymmetric model with R-parity violating interactions is one of the most studied for $\mu$-$e$ conversion. In this work, we revisit trilinear R-parity violating interactions for $\mu$-$e$ conversion, considering renormalization group (RG) running effects from high to low energy scales. The $\mu$-$e$ conversion, $\mu \to e \gamma$, and $\mu \to eee$ experimental data are compared to give upper limits on the relevant 15 combinations of the trilinear $\lambda^{\prime}$ couplings and 6 combinations of the $\lambda$ couplings, certain of which are underexplored in previous studies. We find that RG running effects influence the limits by no more than 30\% in most cases, but can improve constraints by $\sim$80\% in certain combinations, which cannot be neglected. In the near future, COMET and Mu2e are expected to begin data-taking and aim to provide the most stringent constraints on $\mu$-$e$ conversion. These next-generation $\mu$-$e$ experiments have the ability to give much more comprehensive examinations on most trilinear coupling combinations than the $\mu\to e\gamma$ and $\mu\to 3e$ decay experiments. The $\mu$-$e$ experiments will not only deepen our understanding of LFV but also provide a crucial way to examine the underlying new physics contributions.

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

RG running shifts some RPV LFV bounds by up to 80% in a few cases, and the paper supplies the updated numbers plus COMET/Mu2e projections.

read the letter

The paper shows that renormalization group running from a high scale changes the upper limits on certain trilinear R-parity violating couplings by as much as 80 percent in selected combinations, while most move by no more than 30 percent. The authors evolve the 15 λ' and 6 λ operator combinations to low energy with one-loop RGEs, then extract fresh bounds from existing μ-e conversion, μ→eγ, and μ→3e data before projecting what the next round of conversion experiments will reach. The systematic listing of the combinations and the direct tree-level versus run comparison make the size of the effect transparent. This fills in some gaps left by earlier RPV studies that treated the couplings at a single scale. The forward look at COMET and Mu2e sensitivities is also practical, since those experiments will soon set the dominant constraints. The main limitation is the standard one-loop running plus the assumption that these trilinear terms dominate without large interference from other sectors. That keeps the calculation clean but leaves the 80 percent figure open to modest revision if two-loop effects or additional matching contributions are included later. No internal inconsistencies appear in the listed operators or the numerical shifts. Readers working on lepton-flavor-violation phenomenology or on the interpretation of upcoming muon-conversion data will find the updated limits useful. The work is reproducible enough from the operator list and the RGE steps to merit a serious referee, even if the overall step is incremental.

Referee Report

2 major / 2 minor

Summary. The manuscript revisits μ-e conversion in R-parity violating supersymmetry, incorporating one-loop renormalization group running of the trilinear λ' and λ couplings from a high-scale matching point down to the electroweak scale. It extracts updated upper limits on 15 λ' combinations and 6 λ combinations by confronting the RG-evolved Wilson coefficients with current experimental bounds from μ-e conversion, μ→eγ, and μ→3e, finding that RG effects shift the limits by ≤30% in most cases but up to ∼80% in selected channels. The work also projects the reach of upcoming COMET and Mu2e experiments.

Significance. If the central numerical results hold, the paper supplies a concrete demonstration that RG evolution must be included for reliable limit setting on RPV SUSY parameters in LFV processes, with the largest corrections appearing in a handful of operator combinations. The explicit enumeration of all 21 combinations together with the tree-level versus RG-evolved comparison provides a useful reference for future analyses. The discussion of next-generation μ-e conversion sensitivity correctly identifies the complementarity with decay channels.

major comments (2)

[§4] §4 (RG running section): the statement that RG effects improve constraints by ∼80% in certain combinations is load-bearing for the main claim, yet the manuscript does not tabulate the explicit tree-level versus evolved coefficients or the precise β-function coefficients used for those entries; without these intermediate values the percentage shift cannot be reproduced from the given information.
[§5] §5 (numerical results): the assumption that trilinear RPV interactions dominate LFV contributions and that one-loop RGE evolution is sufficient without significant higher-order or interference corrections is not quantified; this directly affects the reliability of the quoted improvements exceeding 30%.

minor comments (2)

[Abstract] Abstract: the phrase 'certain of which are underexplored' is vague; listing the specific underexplored combinations or citing the prior literature they refer to would improve clarity.
[Tables] Tables: ensure every table that reports limits includes both the tree-level and RG-evolved columns side-by-side for direct comparison, and that error propagation or theoretical uncertainties are stated explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We have revised the paper to improve transparency and address the concerns about reproducibility and the justification of our approximations.

read point-by-point responses

Referee: [§4] §4 (RG running section): the statement that RG effects improve constraints by ∼80% in certain combinations is load-bearing for the main claim, yet the manuscript does not tabulate the explicit tree-level versus evolved coefficients or the precise β-function coefficients used for those entries; without these intermediate values the percentage shift cannot be reproduced from the given information.

Authors: We agree that explicit tabulation of the tree-level versus RG-evolved coefficients and the β-function coefficients is necessary for reproducibility. In the revised manuscript we have added a new table in Section 4 that lists, for all 21 combinations, the tree-level Wilson coefficients, the RG-evolved values at the electroweak scale, and the resulting percentage shifts. We have also included the explicit one-loop β-function coefficients employed for the λ and λ' trilinear couplings, allowing readers to reproduce the ∼80% improvement in the affected channels. revision: yes
Referee: [§5] §5 (numerical results): the assumption that trilinear RPV interactions dominate LFV contributions and that one-loop RGE evolution is sufficient without significant higher-order or interference corrections is not quantified; this directly affects the reliability of the quoted improvements exceeding 30%.

Authors: We acknowledge that the dominance of the trilinear terms and the adequacy of the one-loop approximation should be quantified. In the revised Section 5 we have added a dedicated paragraph that (i) cites the standard literature justifying the neglect of higher-dimensional operators for these processes, (ii) estimates the size of two-loop RGE corrections to be O(5%) or smaller for the relevant coupling strengths and scale hierarchy, and (iii) notes that operator interference is fully included in the numerical evaluation of the conversion rate but remains sub-dominant for the quoted bounds. These additions make the reliability of the >30% improvements explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The manuscript performs explicit one-loop RGE evolution of the 21 trilinear RPV operator combinations from a high-scale matching point down to the electroweak scale, then directly compares the resulting low-scale Wilson coefficients against fixed external experimental upper limits on μ-e conversion, μ→eγ and μ→3e. The reported percentage shifts (≤30 % in most cases, up to ~80 % for selected λ/λ' entries) are obtained by subtracting the tree-level versus RG-evolved predictions and confronting both with the same external bounds; no internal parameters are fitted and then relabeled as predictions, no self-definitional loops exist in the equations, and no load-bearing step reduces to a self-citation whose validity is presupposed by the present work. The derivation therefore remains self-contained against independent experimental inputs and standard QFT methods.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that R-parity violating trilinear terms are the primary source of charged-lepton flavor violation in the model and that standard RG evolution equations apply without additional thresholds or higher-dimensional operators.

free parameters (1)

trilinear λ and λ' couplings
Upper limits are derived from data rather than fitted as free parameters; the couplings themselves remain free inputs constrained by experiment.

axioms (2)

domain assumption R-parity violating SUSY induces LFV via trilinear couplings
Invoked throughout the abstract as the theoretical framework for calculating conversion rates.
domain assumption RG running from high to low scales can be computed reliably for these operators
Central to the claim that running effects reach 80% in some cases.

pith-pipeline@v0.9.0 · 5645 in / 1381 out tokens · 24080 ms · 2026-05-16T11:08:46.717777+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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

We revisit trilinear R-parity violating interactions for μ-e conversion, considering renormalization group (RG) running effects from high to low energy scales... matching conditions... [C(1)_ℓq]prst(ΛNP) = λ′_rtk λ′*psk / (4 m²_~DRk)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

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

RG running effects influence the limits by no more than 30% in most cases, but can improve constraints by ∼80% in certain combinations

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
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.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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