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arxiv: 2204.00564 · v3 · pith:QHRIHLIEnew · submitted 2022-04-01 · ✦ hep-ph

Reach and complementarity of μto e searches

Sacha Davidson , Bertrand Echenard This is my paper

Pith reviewed 2026-05-24 11:50 UTC · model grok-4.3

classification ✦ hep-ph
keywords muon electron conversionflavor violationeffective field theorynew physics scalemu to e gammamu to 3eoperator complementaritynucleon currents
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0 comments X

The pith

Effective field theory organizes muon-electron flavor violation into a six-dimensional space where three experiments give complementary constraints on new physics.

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

The paper works in effective field theory to describe transitions that change a muon into an electron. It selects an operator basis tied directly to measurable processes and isolates a six-dimensional subspace covered by the decays to a photon, to three electrons, and to electron conversion inside nuclei. Within that subspace the authors translate current and projected experimental limits into bounds on the scale of new physics. The three channels together fill out the space in a way that no single measurement can achieve alone. The work also notes that separating scalar operators acting on up versus down quarks will require more precise knowledge of the nucleon's quark content.

Core claim

In the six-dimensional subspace of effective operators probed by μ→eγ, μ→3e and μ→e conversion, existing and planned experiments set limits on the new physics scale; the processes are complementary because each is sensitive to a different linear combination of the six coefficients.

What carries the argument

A six-dimensional subspace of effective field theory operators for μ-e flavor-changing neutral currents, chosen so that each experimental observable maps onto a distinct direction in coefficient space.

If this is right

  • Future sensitivities will push the new-physics scale bound higher across the entire six-dimensional space.
  • No single channel can exclude all directions; all three measurements are required for full coverage.
  • Scalar operators acting on up versus down quarks remain degenerate until nucleon scalar currents are known to higher precision.
  • The same operator basis can be used to compare the reach of different nuclear targets in conversion experiments.

Where Pith is reading between the lines

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

  • The same six-dimensional picture could be applied to tau-lepton flavor violation to see whether the complementarity pattern repeats.
  • If a signal appears, the relative rates among the three channels would point to which linear combination of operators is nonzero.
  • Lattice calculations that reduce uncertainty on the nucleon scalar form factors would immediately sharpen the distinction between up- and down-quark scalar interactions.

Load-bearing premise

The chosen set of operators fully accounts for all new physics contributions that can affect the three observables, without missing terms or needing higher-dimensional corrections.

What would settle it

A measured rate in one of the three channels that lies outside the range allowed by any combination of the six coefficients at a given new-physics scale would show the subspace is incomplete.

Figures

Figures reproduced from arXiv: 2204.00564 by Bertrand Echenard, Sacha Davidson.

Figure 1
Figure 1. Figure 1: FIG. 1. Reach as a function of (left) the angle [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reach as a function of the angle [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Reach as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reach as a function of the angle [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Reach as a function of the angle [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Normalised quark (solid) and nucleon (dotted) overlap integrals as a function of the target charge [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Misalignement angle between target vectors, calculated for quarks and nucleons. Notice the reduced vertical scale and [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

In Effective Field Theory, we describe $\mu\leftrightarrow e$ flavour changing transitions using an operator basis motivated by experimental observables. In a six-dimensional subspace probed by $\mu \to e \gamma$, $\mu \to 3e$ and $\mu\to e$ conversion on nuclei, we derive constraints on the New Physics scale from past and future experiments, illustrating the complementarity of the processes in an intuitive way. We also recall that a precise determination of the scalar quark currents in the nucleon will be required to distinguish scalar $\mu\to e$ interactions on u-quarks from those on d-quarks.

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

1 major / 0 minor

Summary. The paper describes μ↔e flavour changing transitions in Effective Field Theory using an operator basis motivated by experimental observables. In a six-dimensional subspace probed by μ → e γ, μ → 3e and μ→e conversion on nuclei, constraints on the New Physics scale are derived from past and future experiments to illustrate complementarity. It also recalls that precise determination of scalar quark currents in the nucleon is required to distinguish scalar μ→e interactions on u-quarks from those on d-quarks.

Significance. If the central results hold, the work offers an intuitive illustration of complementarity among μ→e processes, aiding in the interpretation of current and future experimental results. Credit is given for tying the operator basis directly to observables and highlighting the role of nucleon matrix elements. The analysis is useful for the hep-ph community working on flavour physics and lepton flavour violation.

major comments (1)
  1. [Abstract] Abstract: The abstract provides no indication that the one-loop anomalous-dimension matrix was computed or that mixing from operators outside the 6D subspace was included under renormalization-group evolution. Since the central claim involves deriving constraints on the New Physics scale within this subspace, this omission is load-bearing if mixing occurs, as is generic for dimension-6 operators.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive comment on the abstract. We address the point below and have revised the manuscript to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The abstract provides no indication that the one-loop anomalous-dimension matrix was computed or that mixing from operators outside the 6D subspace was included under renormalization-group evolution. Since the central claim involves deriving constraints on the New Physics scale within this subspace, this omission is load-bearing if mixing occurs, as is generic for dimension-6 operators.

    Authors: We agree that the abstract should make the scope of the analysis explicit. Our study is confined to the six-dimensional subspace of operators directly probed by the listed observables. Constraints on the New Physics scale are obtained by working within this subspace at the relevant low-energy scales; we neither compute the full one-loop anomalous-dimension matrix nor incorporate mixing from operators outside the subspace. This choice aligns with the paper's focus on complementarity among the processes that probe the chosen basis. We have revised the abstract to state this limitation clearly. revision: yes

Circularity Check

0 steps flagged

No circularity; EFT constraints derived from external experimental inputs

full rationale

The paper selects a 6D operator subspace motivated by the three observables (μ→eγ, μ→3e, μ→e conversion), then extracts NP-scale bounds directly from measured and projected experimental limits. This is a standard EFT mapping with no reduction of the central result to a fitted parameter renamed as prediction, no self-definitional loop, and no load-bearing self-citation chain. The derivation chain remains open to external data and does not close on itself by construction. The skeptic concern about RG mixing is a completeness question, not a circularity issue.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract, the main assumption is the validity and completeness of the EFT approach for flavor changing transitions.

axioms (1)
  • domain assumption The EFT operator basis is complete for the described processes
    Assumed in the description of the six-dimensional subspace

pith-pipeline@v0.9.0 · 5618 in / 1127 out tokens · 27201 ms · 2026-05-24T11:50:58.104773+00:00 · methodology

discussion (0)

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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
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    In Effective Field Theory, we describe μ↔e flavour changing transitions using an operator basis motivated by experimental observables. In a six-dimensional subspace probed by μ→eγ, μ→3e and μ→e conversion on nuclei, we derive constraints on the New Physics scale from past and future experiments

  • IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The degree of complementarity can be evaluated at ΛLFV by translating the coefficients in eqn (II.1) from the experimental scale to ΛLFV via the Renormalisation Group Equations (RGEs)

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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