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arxiv: 2606.08268 · v1 · pith:GBPB7VUWnew · submitted 2026-06-06 · ✦ hep-ph

Electron-muon colliders at high energies to discover heavy sterile neutrinos

Gorazd Cveti\v{c} , Claudio Dib , C. S. Kim , K. N. Vishnudath This is my paper

Pith reviewed 2026-06-27 19:21 UTC · model grok-4.3

classification ✦ hep-ph
keywords sterile neutrinoselectron muon collidercharged lepton flavor violationW boson pair productiontype-I seesawneutrino mixing bounds
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The pith

High-energy e-μ collisions can detect heavy sterile neutrinos via W-pair production

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

The paper investigates charged-lepton-flavor-violating scattering of electrons and muons to search for heavy sterile neutrinos. Below the W-pair threshold the signal process proceeds through loop diagrams and is suppressed by four powers of the small mixing angle between active and sterile neutrinos. Above threshold the process producing two W bosons allows much larger rates that remain within current experimental bounds on the mixing. This makes the high-energy channel the more promising one for discovery at proposed electron-muon colliders in both single-sterile and type-I seesaw models.

Core claim

For center-of-mass energies above 2 M_W the process e^- μ^+ → W^+ W^- provides a viable probe for heavy sterile neutrinos, with cross sections that can be observable given present constraints on active-sterile mixing, whereas the lower-energy process e^- μ^+ → e^+ μ^- is strongly suppressed by quartic mixing dependence.

What carries the argument

Heavy sterile neutrino exchange diagrams contributing to the high-energy e^- μ^+ → W^+ W^- process

If this is right

  • The W-pair channel gives cross sections orders of magnitude above the loop-induced process
  • Observable signals are possible at future e-μ colliders without violating existing mixing bounds
  • Results hold for both a single heavy sterile neutrino and the minimal type-I seesaw scenario

Where Pith is reading between the lines

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

  • Designs for electron-muon colliders should aim for energies well above the W threshold to exploit this channel
  • The same mechanism could be studied in other lepton flavor combinations or at different collider types
  • Limits from non-observation would directly constrain sterile neutrino parameters in a new way

Load-bearing premise

Current upper limits on active-sterile neutrino mixing angles can be applied straightforwardly to calculate the maximum possible rates for the new processes

What would settle it

A precise measurement at an e-μ collider finding the W-pair production rate substantially lower than the maximum value allowed by present mixing bounds would show that the process is not as promising as calculated

Figures

Figures reproduced from arXiv: 2606.08268 by Claudio Dib, C. S. Kim, Gorazd Cveti\v{c}, K. N. Vishnudath.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Some Feynman diagrams that contribute to the process [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Feynman diagrams for the scattering process [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Variation of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Predictions for light–heavy mixing as a function of the heavy neutrino mass in the minimal type-I seesaw model with [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Variation of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Variation of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
read the original abstract

We study high-energy charged-lepton-flavor-violating (cLFV) channels in $e^- \mu^+$ scattering to probe heavy sterile neutrinos, which arise naturally in minimal extensions of the Standard Model. For $\sqrt{s} \le 2M_W$, we consider the process $e^- \mu^+ \to e^+ \mu^-$, which is dominated by one-loop box diagrams. We numerically evaluate these diagrams, involving a high-energy extension of the Inami-Lim functions, and find that the amplitudes are strongly suppressed because of their quartic dependence on light-heavy mixing. Using current bounds on active-sterile neutrino mixing, we determine the maximal rates allowed by existing constraints. For $\sqrt{s} > 2M_W$, we analyze the process $e^- \mu^+ \to W^+ W^-$ and compute the corresponding cross sections in both single-sterile and minimal type-I seesaw scenarios. We find this latter process to be significantly more promising for revealing the presence of heavy sterile neutrinos at $e-\mu$ colliders.

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

0 major / 2 minor

Summary. The manuscript studies charged-lepton-flavor-violating processes in high-energy e−μ+ scattering to probe heavy sterile neutrinos. For √s ≤ 2MW it numerically evaluates one-loop box diagrams for e−μ+ → e+μ− using a high-energy extension of the Inami-Lim functions and finds strong quartic suppression from active-sterile mixing; maximal rates are set using existing experimental bounds. For √s > 2MW it computes cross sections for e−μ+ → W+W− in both the single-sterile-neutrino case and the minimal type-I seesaw, concluding that the latter channel is significantly more promising for discovery at e-μ colliders.

Significance. If the one-loop evaluations and cross-section results hold, the work identifies a collider channel with reduced suppression relative to low-energy cLFV, potentially offering improved sensitivity to heavy steriles within current mixing limits. Explicit computation in both single-sterile and type-I seesaw scenarios provides a concrete check on model-dependent effects.

minor comments (2)
  1. Abstract states that both single-sterile and minimal type-I seesaw scenarios are computed for the WW channel; the manuscript should include an explicit subsection (e.g., §4) showing how the seesaw relation is imposed on the mixing matrix and whether any cancellations appear in the amplitudes.
  2. The numerical stability of the high-energy Inami-Lim extension and the treatment of integration errors or cutoff dependence should be documented, as the low-energy process is reported to be strongly suppressed.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. The provided summary accurately reflects the scope and conclusions of the manuscript. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No circularity: cross sections computed from standard extensions and external bounds

full rationale

The paper evaluates cLFV amplitudes via one-loop diagrams (extended Inami-Lim functions) and computes cross sections for e-μ → W+W− in both single-sterile and minimal type-I seesaw cases. Maximal rates are set by applying published experimental limits on active-sterile mixing; these limits are external inputs, not fitted or redefined within the work. No step equates a derived quantity to its own input by construction, renames a known result, or relies on a load-bearing self-citation whose validity is presupposed. The derivation chain remains independent of the target observables.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the standard type-I seesaw framework and external experimental limits on mixing angles; no new free parameters are introduced beyond those bounds.

free parameters (1)
  • active-sterile mixing parameters
    Maximal rates are set by existing experimental upper limits on these angles rather than being derived inside the paper.
axioms (1)
  • domain assumption Minimal type-I seesaw model correctly parametrizes heavy sterile neutrinos
    Both single-sterile and minimal type-I seesaw scenarios are analyzed as the theoretical setting.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Torsional four-fermion interaction for Majorana neutrinos

    hep-ph 2026-06 unverdicted novelty 4.0

    Torsion-induced four-fermion interactions modify effective masses and mixing parameters for Majorana neutrinos with sterile partners in matter.

Reference graph

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