arxiv: 2604.12844 · v1 · submitted 2026-04-14 · ✦ hep-ph

Recognition: unknown

Operator Identification in Charged Lepton-Flavor Violation: Global EFT Analysis with RG Evolution, Polarization Observables, and Bayesian Model Discrimination at Future Colliders

Nicol\'as Viaux M

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:34 UTC · model grok-4.3

classification ✦ hep-ph

keywords charged lepton flavor violationeffective field theoryrenormalization group evolutionoperator identificationfuture colliderspolarization observablesbayesian model discriminationleptoquarks

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The pith

A global effective field theory analysis with renormalization-group running and polarization data can identify specific operators behind charged lepton-flavor violation at future colliders.

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

The paper sets out a combined fit of low-energy bounds and collider observables from FCC-ee, ILC, CLIC, HL-LHC, HE-LHC and muon colliders to isolate the effective operators that could produce charged lepton-flavor violation. One-loop renormalization-group evolution is run between the multi-TeV matching scale and the measurement scale, producing 10-30 percent shifts in the correlation pattern among operators. Polarization asymmetries are shown to break degeneracies between two scalar operators, while Bayes factors quantify how cleanly the data can tell leptoquark models apart from heavy-neutral-lepton models. A reader would care because lepton-flavor violation is one of the cleanest null tests of the Standard Model; knowing which operator is active would directly point to the type of new physics that must be built.

Core claim

By mapping ultraviolet-matched Wilson coefficients through one-loop renormalization-group running to the collider measurement scale, incorporating polarization asymmetries in e+e- and muon-collider channels, and performing a global profile-likelihood fit that also includes Dalitz-level μ→3e information, the analysis demonstrates that operator directions can be resolved and that Bayes factors can discriminate between representative leptoquark and heavy-neutral-lepton ultraviolet completions.

What carries the argument

The global profile-likelihood framework that evolves operator coefficients via one-loop renormalization-group running and uses polarization asymmetries to separate operator directions.

If this is right

Renormalization-group evolution produces 10-30 percent shifts in selected operator-correlation entries when multi-TeV matching scales are used.
Polarization asymmetries cleanly separate the c_Hℓ and c_He operator directions.
Bayes factors provide quantitative discrimination between leptoquark and heavy-neutral-lepton ultraviolet hypotheses.
Event-level generation and detector simulation for hadron and muon colliders yield realistic projections for operator identification.

Where Pith is reading between the lines

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

If an operator is identified, the measured coefficient would translate into a preferred range for the mass scale of the underlying new physics.
The same global framework could be applied to other rare processes such as τ→3μ or μ-e conversion to test consistency across channels.
Absence of a signal would still tighten operator bounds beyond what exclusion limits alone provide, because the fit exploits correlations among observables.

Load-bearing premise

The effective field theory remains valid up to the multi-TeV scales of the colliders and the two chosen benchmark models capture the relevant new-physics effects.

What would settle it

A statistically significant sample of charged lepton-flavor violating events whose measured angular distributions or rates lie outside the bands predicted by the renormalization-group-evolved operator set, or a data set in which the Bayes factor between the two benchmark ultraviolet models remains close to one despite high luminosity.

Figures

Figures reproduced from arXiv: 2604.12844 by Nicol\'as Viaux M.

**Figure 2.** Figure 2: FIG. 2. Expanded 9 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 4.** Figure 4: shows the significance evolution across cutflow stages and confirms that the largest gains are obtained when topology and MVA selections are combined [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Complementarity contours in the ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Profile-likelihood scan in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. EFT-validity stress test in which the vertical axis [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Reconstructed [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Representative one-loop running-matrix entries as a [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Polarization-resolved confidence ellipses in the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Dalitz-template panels in ( [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Discovery-injection identification contours in the [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. Run-plan optimization map using determinant [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. Impact of correlated systematic uncertainty on [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. Projection of two UV-inspired model bands onto the [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗

read the original abstract

Charged lepton-flavor violation is a null-test frontier of the Standard Model and a direct probe of physics beyond it. We present a global effective field theory (EFT) analysis across FCC-ee, ILC, CLIC, HL-LHC, HE-LHC, and muon colliders at 3 and 10 TeV, with operator identification as the primary target rather than exclusion reach alone. The analysis combines low-energy constraints, collider differential observables, and Dalitz-level $\mu\to 3e$ information in a common profile-likelihood framework. Key hadron-collider and muon-collider signal/background samples are generated at event level and propagated through Delphes detector simulation, while clean $e^+e^-$ benchmark channels are modeled with CDR-calibrated parametric response. We include one-loop renormalization-group (RG) running and operator mixing between UV matching and measurement scales, finding 10--30\% shifts in selected operator-correlation entries when comparing tree-level and RG-evolved coefficient mappings at multi-TeV matching scales. Polarization asymmetries are used to separate $c_{H\ell}$ and $c_{He}$ directions, and UV discrimination is quantified with Bayes factors for benchmark leptoquark and heavy-neutral-lepton hypotheses. The full code chain for event generation, detector response, inference, and figure reproduction is provided.

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

This paper sets up a global EFT fit for charged LFV that includes explicit one-loop RG running with 10-30% shifts and uses polarization to separate operators, all with code released.

read the letter

The main takeaway is that this work builds a global EFT analysis for charged lepton-flavor violation across multiple future colliders, folding in one-loop RG evolution from multi-TeV matching scales down to measurement points and using polarization asymmetries to pull apart directions like c_Hℓ and c_He. It also runs Bayesian discrimination on benchmark UV models such as leptoquarks and heavy neutral leptons. The RG shifts in operator correlations are quantified at 10-30%, which is a concrete output rather than a side note. They tie low-energy constraints, collider differential observables, and Dalitz-level μ→3e data into one profile-likelihood setup. Event samples for hadron and muon colliders go through Delphes, while e+e- channels use parametric responses calibrated to CDR. The full code chain for generation, simulation, inference, and figures is provided, which makes the results checkable. The operator basis and anomalous-dimension matrices are laid out explicitly, and the scale choices for running look consistent with the stated goals. The central claims hold up on the details given, with no internal contradictions in the RG implementation or the separation method. The soft spots sit mostly in the framing assumptions. The EFT is taken to remain valid up to multi-TeV scales, which is standard but means any UV effects above that are outside scope. The UV benchmarks are presented as illustrative, so the Bayes factors show how the method works rather than delivering strong model exclusion. Choices around data cuts or simulation settings could be probed in review, but nothing appears load-bearing or inconsistent. This paper is for EFT phenomenologists and experimentalists focused on LFV operator identification at FCC-ee, ILC, CLIC, HL-LHC, HE-LHC, and muon colliders. A reader who wants a ready framework that goes beyond simple limits and includes RG mixing and polarization will find it useful. It deserves serious referee time because the technical pieces are in place and the results are reproducible. I recommend sending it for peer review.

Referee Report

0 major / 3 minor

Summary. The paper presents a global effective field theory analysis of charged lepton-flavor violation across future colliders (FCC-ee, ILC, CLIC, HL-LHC, HE-LHC, and muon colliders at 3 and 10 TeV). Operator identification is the primary goal, achieved via a profile-likelihood framework that combines low-energy constraints, collider differential observables, and Dalitz-level μ→3e information. The analysis incorporates one-loop RG running and operator mixing (reporting 10–30% shifts in selected operator correlations at multi-TeV matching scales), uses polarization asymmetries to separate c_{Hℓ} and c_{He} directions, and quantifies UV model discrimination via Bayes factors for benchmark leptoquark and heavy-neutral-lepton hypotheses. Event-level generation and Delphes simulation are used for hadron and muon colliders, with full code provided for reproducibility.

Significance. If the results hold, the work advances cLFV phenomenology by shifting focus from exclusion limits to concrete operator identification and UV discrimination in a multi-scale, multi-observable setting. The explicit inclusion of one-loop RG evolution with mixing, polarization observables for operator separation, and Bayesian quantification are useful additions. The provision of the complete code chain for event generation, detector response, inference, and figure reproduction is a clear strength that supports reproducibility and community follow-up.

minor comments (3)

[Abstract and § on e⁺e⁻ modeling] The abstract refers to 'CDR-calibrated parametric response' for e⁺e⁻ channels; the main text should define CDR and provide explicit details on the calibration procedure and its validation against full simulation.
[RG evolution section] While the operator basis and one-loop anomalous-dimension matrices are supplied, a dedicated table or figure directly comparing tree-level versus RG-evolved coefficient mappings (with numerical shifts) would strengthen the central 10–30% claim.
[UV discrimination section] The benchmark UV models are described as illustrative; the text should explicitly state the operator mappings assumed for each (leptoquark and heavy neutral lepton) to allow readers to reproduce the Bayes-factor inputs.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately reflects the scope of our global EFT analysis of charged lepton-flavor violation, including the incorporation of RG running, polarization observables, and Bayesian discrimination across multiple future colliders. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The manuscript supplies the operator basis, explicit one-loop anomalous-dimension matrices, profile-likelihood construction, and full event-generation plus Delphes pipeline. The reported 10-30% RG-induced shifts in operator correlations are obtained by direct application of the provided one-loop running and mixing between stated matching and measurement scales, not by fitting a parameter and relabeling the output as a prediction. Polarization asymmetries separate c_Hℓ and c_He directions via collider observables independent of the UV benchmarks. Bayesian discrimination is performed on illustrative leptoquark and heavy-neutral-lepton hypotheses presented as examples rather than exhaustive or self-fitted models. No self-citation chain, definitional equivalence, or fitted-input-renamed-as-prediction appears in the load-bearing steps; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard EFT validity at collider scales and benchmark UV models for discrimination; coefficients are fitted parameters in the likelihood framework.

free parameters (1)

EFT operator coefficients
Fitted within the profile-likelihood framework to combined low-energy and collider constraints.

axioms (1)

domain assumption Effective field theory provides a valid description of new physics up to multi-TeV collider energies
Invoked for UV matching and RG evolution between scales.

pith-pipeline@v0.9.0 · 5546 in / 1473 out tokens · 50510 ms · 2026-05-10T14:34:08.299942+00:00 · methodology

discussion (0)

Reference graph

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