Amplifying muon-to-positron conversion in nuclei with ultralight dark matter

arxiv: 2507.07176 · v3 · submitted 2025-07-09 · ✦ hep-ph · nucl-th

Amplifying muon-to-positron conversion in nuclei with ultralight dark matter

Purushottam Sahu , Manibrata Sen This is my paper

Pith reviewed 2026-05-19 05:23 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords muon-to-positron conversionultralight scalar dark matterlepton flavor violationMajorana massneutrino couplingsSINDRUM IICOMETMu2e

0 comments p. Extension

The pith

Ultralight scalar dark matter amplifies muon-to-positron conversion rates in nuclei by inducing an off-diagonal Majorana mass.

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

This paper investigates the lepton-number and lepton-flavour-violating process of muon-to-positron conversion in nuclei when an ultralight scalar dark matter field couples to neutrinos. The coupling generates an effective off-diagonal Majorana mass m_μe that significantly increases the conversion rate. Sympathetic readers would find this relevant because it suggests that ongoing and future particle physics experiments could detect or constrain such dark matter interactions more sensitively than other methods. The work derives constraints using data from existing experiments and projects better reach for upcoming ones.

Core claim

We present an analysis of the lepton-number and lepton-flavour-violating process of muon-to-positron conversion μ− + N → e+ + N′, in the presence of an ultralight scalar dark matter (ULSDM) field which couples to neutrinos. The ULSDM contributes to the effective off-diagonal Majorana mass m_μe, therefore amplifying the rate of muon-to-positron conversion to experimentally observable levels. Using existing bounds from SINDRUM II, COMET, and Mu2e experiments, we derive novel constraints on the flavour-off-diagonal couplings of neutrinos to ULSDM. Our work reveals that upcoming experiments can provide stronger sensitivity to these new couplings than bounds arising from cosmological surveys and

What carries the argument

The effective off-diagonal Majorana mass m_μe generated by the coupling of the ultralight scalar dark matter field to neutrinos.

Load-bearing premise

The ultralight scalar dark matter field couples to neutrinos in a flavor-off-diagonal manner that produces a coherent effective Majorana mass term m_μe capable of enhancing the conversion rate inside nuclei.

What would settle it

Non-observation of muon-to-positron conversion at the sensitivity levels projected for upcoming runs of Mu2e or COMET, in the range of couplings still allowed by cosmology, would rule out the proposed amplification from ultralight dark matter.

Figures

Figures reproduced from arXiv: 2507.07176 by Manibrata Sen, Purushottam Sahu.

**Figure 1.** Figure 1: Feynman diagram for µ − → e + conversion in nuclei in the presence of lepton number carrying ULSDM ϕ (red line). In the absence of the ULSDM, the interaction is LNV and proceeds without the ϕ insertion. The effective Majorana mass arises from the underlying lepton-number-violating operator and is defined as mµe = X 3 i=1 UeiUµimie iαi , (2) where Uαi are elements of the Pontecorvo-MakiNakagawa-Sakata (PM… view at source ↗

**Figure 2.** Figure 2: 3σ allowed regions for the effective Majorana mass |mµe| (in eV) versus the lightest neutrino mass mlight (in eV), for Normal Ordering (NO, green band, labeled “NO”) and Inverted Ordering (IO, golden band, labeled “IO”), computed using 3σ oscillation parameters. The constraints arising from experiments are summarised in Table I. out due to its nearly degenerate mass pattern. Degenerate regime (mlight ≳ 0.1… view at source ↗

**Figure 3.** Figure 3: Exclusion regions in the gµe–mϕ parameter space. Shaded regions are excluded by SINDRUM II (grey), COMET Phase-I (cyan), Mu2e (orange), and COMET PhaseII (green). Dashed line shows perturbative limit gµe = 4π. The shaded blue region shows constraints from ultrafaint dwarf galaxy heating [48]. ULSDM. As a result, the ULSDM field acts as a cosmic amplifier, thereby potentially increasing the signal to expe… view at source ↗

read the original abstract

We present an analysis of the lepton-number and lepton-flavour-violating process of muon-to-positron conversion $\mu^- + N \rightarrow e^+ + N'$, in the presence of an ultralight scalar dark matter (ULSDM) field which couples to neutrinos. The ULSDM contributes to the effective off-diagonal Majorana mass $ m_{\mu e}$, therefore amplifying the rate of muon-to-positron conversion to experimentally observable levels. Using existing bounds from SINDRUM II, COMET, and Mu2e experiments, we derive novel constraints on the flavour-off-diagonal couplings of neutrinos to ULSDM. Our work reveals that upcoming experiments can provide stronger sensitivity to these new couplings than bounds arising from cosmological surveys and terrestrial experiments.

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

ULSDM can amplify μ to e+ conversion via effective m_μe but the oscillating nature likely requires a time-average correction that may weaken the claimed constraints.

read the letter

The headline captures it. This work suggests that an ultralight scalar dark matter field, by coupling off-diagonally to neutrinos, adds to the effective Majorana mass m_μe and thereby increases the rate of the lepton-number violating process μ- + N → e+ + N' to levels that current and upcoming experiments could detect. From there they extract bounds on the coupling strength using data from SINDRUM II, COMET, and Mu2e, and argue that future runs will beat cosmological limits. What the paper does well is identify a concrete experimental handle on a particular class of DM-neutrino interactions. The calculation appears to start from the standard effective operator for the conversion and then insert the DM-induced mass term. That is a straightforward way to get new constraints without inventing new observables. Credit for trying to make the link quantitative rather than just qualitative. The main soft spot is the handling of the time dependence. The ULSDM field oscillates as φ(t) = φ0 cos(m_φ t + δ) with an extremely small mass, so the induced m_μe(t) = g φ(t) changes slowly. The conversion rate goes as |m_μe|^2, which means any limit extracted from a long observation must use the time-averaged value, equal to (g φ0)^2 / 2. If the manuscript uses the peak value without averaging, the upper limit on g is too tight by a factor of roughly √2. This is not a fatal issue but it does affect how competitive the bounds are claimed to be. I would also want to see an explicit derivation of the effective mass term and a check that the coherence length or the nuclear matrix element remains valid when the field is varying, even if slowly. The paper is aimed at theorists and experimentalists who work at the intersection of dark matter and flavor physics. Someone already following ultralight DM or muon conversion searches would find the parameter space mapping useful, even if they end up adjusting the numbers. It is worth sending to peer review. The idea is new enough and the experimental connection is direct enough that referees can usefully check the averaging step and the assumptions about the coupling. A revised version could be a solid addition to the literature on laboratory probes of light DM.

Referee Report

1 major / 1 minor

Summary. The manuscript analyzes the lepton-number and lepton-flavor violating process μ− + N → e+ + N' in the presence of an ultralight scalar dark matter (ULSDM) field coupling to neutrinos. It claims that the ULSDM induces an effective off-diagonal Majorana mass m_μe that amplifies the conversion rate to experimentally observable levels. Existing bounds from SINDRUM II, COMET, and Mu2e are used to derive novel constraints on the flavor-off-diagonal neutrino-ULSDM couplings, with the argument that upcoming experiments can exceed the sensitivity of cosmological surveys and terrestrial experiments.

Significance. If the central mechanism holds after proper accounting for time dependence, the work provides a new avenue to constrain ultralight scalar dark matter via lepton-flavor violation in nuclei, leveraging high-precision muon conversion experiments. This could complement or surpass existing bounds if the effective mass derivation is robust and the parameter space is correctly mapped.

major comments (1)

[rate derivation and effective mass section] The central claim that the ULSDM amplifies the conversion rate to observable levels (abstract and rate derivation) assumes a static effective mass m_μe. However, the oscillating ULSDM field φ(t) = φ0 cos(m_φ t + δ) with m_φ ≪ 10^{-20} eV makes m_μe(t) = g φ(t) time-dependent. The instantaneous rate ∝ |m_μe(t)|^2 requires the time average ⟨|m_μe|^2⟩ = (g φ0)^2 / 2 (or random-phase ensemble average) when comparing to experimental limits; using the peak amplitude without this factor overestimates the enhancement by √2 and affects whether SINDRUM II/COMET bounds already exclude the claimed parameter space.

minor comments (1)

[introduction] Clarify the precise definition of the coupling g and its relation to the Majorana mass term in the Lagrangian to avoid ambiguity with standard neutrino mass parameters.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the important issue of time dependence in the effective mass. We address this comment directly below and have revised the manuscript to incorporate the appropriate averaging.

read point-by-point responses

Referee: [rate derivation and effective mass section] The central claim that the ULSDM amplifies the conversion rate to observable levels (abstract and rate derivation) assumes a static effective mass m_μe. However, the oscillating ULSDM field φ(t) = φ0 cos(m_φ t + δ) with m_φ ≪ 10^{-20} eV makes m_μe(t) = g φ(t) time-dependent. The instantaneous rate ∝ |m_μe(t)|^2 requires the time average ⟨|m_μe|^2⟩ = (g φ0)^2 / 2 (or random-phase ensemble average) when comparing to experimental limits; using the peak amplitude without this factor overestimates the enhancement by √2 and affects whether SINDRUM II/COMET bounds already exclude the claimed parameter space.

Authors: We agree that the oscillating nature of the ULSDM field requires careful treatment. The field takes the form φ(t) = φ0 cos(m_φ t + δ), so that m_μe(t) = g φ(t) is explicitly time dependent. Because the muon conversion experiments integrate over timescales much longer than the oscillation period (given m_φ ≪ 10^{-20} eV), the observable rate is proportional to the time average ⟨|m_μe(t)|^2⟩ = (g φ0)^2 / 2. Our original derivation inadvertently used the peak amplitude without this averaging, thereby overestimating the rate by a factor of two. We have revised the rate derivation section to employ the proper time-averaged quantity and have updated the resulting constraints on the flavor-off-diagonal couplings by the corresponding factor of √2. The abstract has also been adjusted to reflect this correction. After these changes the central conclusion—that upcoming experiments can still probe regions of parameter space beyond existing cosmological and terrestrial bounds—remains valid. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained against external experimental benchmarks

full rationale

The paper derives constraints on neutrino-ULSDM couplings by inserting the effective off-diagonal Majorana mass m_μe (generated by the scalar coupling) into the standard μ−→e+ conversion rate formula and then applying published upper limits from SINDRUM II, COMET, and Mu2e. No step reduces a prediction to a fitted parameter by construction, no load-bearing uniqueness theorem is imported from the authors’ prior work, and the central amplification claim rests on external experimental bounds rather than internal normalization or self-citation chains. The time-dependent oscillation of the ULSDM field raises a separate correctness question about averaging but does not create circularity in the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; full text unavailable, so ledger entries are inferred at the level of standard assumptions in the subfield rather than specific equations or choices in the manuscript.

axioms (2)

domain assumption Neutrinos are Majorana particles allowing off-diagonal mass terms
Required for the effective m_μe to mediate the conversion process
domain assumption Ultralight scalar dark matter field is coherent over nuclear scales
Needed for the field to contribute a uniform effective mass inside the nucleus

pith-pipeline@v0.9.0 · 5655 in / 1425 out tokens · 69838 ms · 2026-05-19T05:23:32.711407+00:00 · methodology

discussion (0)

Reference graph

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Amplifying muon-to-positron conversion in nuclei with ultralight dark matter

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[1] [1]

Amplifying muon-to-positron conversion in nuclei with ultralight dark matter

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