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REVIEW 2 major objections 3 minor 1 cited by

By adding muon-nucleus scattering to the displaced-vertex search, MUonE can probe new vector bosons up to about 150 MeV, filling a gap in mediator parameter space.

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2026-08-03 23:59 UTC pith:RAQDJDZ5

load-bearing objection Genuinely new and mostly solid projection: μN production at MUonE plausibly extends displaced-vector-boson reach to ~150 MeV; the zero-background assumption and a factor-8 normalization discrepancy are the main caveats, both addressable. the 2 major comments →

arxiv 2511.03222 v2 pith:RAQDJDZ5 submitted 2025-11-05 hep-ph

Filling the Gap: Hunting for Vector Bosons at the MUonE Experiment with Displaced Decay Signature

Duncan Rocha , Isaac R. Wang This is my paper
classification hep-ph
keywords dark photonvector bosondisplaced vertexMUonEmuon scatteringdark bremsstrahlunglong-lived particlehidden sector
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that MUonE, a fixed-target experiment built to measure the running of the electromagnetic coupling via elastic muon-electron scattering, can also serve as a displaced-vertex detector for new long-lived vector bosons. These bosons would be produced by dark bremsstrahlung in either muon-electron or muon-nucleus scattering and decay to an electron-positron pair a few centimeters from the target, a signature that MUonE's precise tracking can reconstruct. The authors combine the two production channels and show that the nuclear channel, with its larger center-of-mass energy, doubles the maximum boson mass the experiment can reach, extending the projected sensitivity from about 70 MeV to roughly 150 MeV for dark-photon-like couplings down to ~1e-5. The analysis covers three well-motivated U(1) extensions of the Standard Model: the dark photon, U(1)_{B-L}, and U(1)_{Le-Lmu}.

Core claim

The paper's central claim is that MUonE's precision tracking can be repurposed as a displaced-vertex search. A vector boson produced in muon scattering can travel 25-140 mm before decaying to an e+e- pair; the two daughters plus the scattered muon must all cross three tracking stations. With a Monte Carlo simulation and assuming zero background, the authors project 95% CL sensitivity to the dark photon mixing down to ~1e-5 for masses up to ~100-150 MeV. The nuclear channel provides the high-mass reach because its 54 GeV center-of-mass energy opens phase space unavailable in muon-electron scattering at 400 MeV. For the gauged U(1)_{B-L} and U(1)_{Le-Lmu} models, invisible neutrino decays redu

What carries the argument

The central mechanism is the displaced-vertex signature: a requirement that the vector boson decay within a 25-140 mm window in front of the target, with the two daughter tracks and the scattered muon all crossing three tracking stations and reaching the ECAL/muon filter for particle identification. The reach comes from the complementarity of two production modes. Muon-electron scattering dominates the cross-section for boson masses below about 60 MeV, while muon-nucleus scattering, with sqrt(s)=54 GeV, enables production of heavier mediators. Using only the last five of the forty modules guarantees that any track crossing all three stations is within the calorimeter acceptance.

Load-bearing premise

The paper assumes zero Standard Model background in both production channels, but that assumption was only tested for the muon-electron channel; the nuclear channel, with its much larger center-of-mass energy, can produce hadronic events that may fake the three-track displaced-vertex topology.

What would settle it

Run a dedicated simulation of muon-nucleus interactions at 54 GeV center-of-mass energy through the MUonE geometry, applying the paper's selection (decay vertex between 25 and 140 mm, daughter energy >1 GeV, opening angle >1 mrad, all three tracks crossing the tracking stations, last five modules). If any K0 → π+π− or Λ → pπ− event passes all cuts per 10^16 muons on target, the zero-background assumption is falsified and the 95% CL sensitivity curves in the paper would need to be redrawn.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the projection holds, MUonE closes the long-standing 'gap' in dark-photon parameter space between collider exclusions and beam-dump limits, for masses from a few MeV to ~150 MeV.
  • Adding the nuclear channel gives a factor of two improvement in the maximum accessible mediator mass compared with using muon-electron scattering alone.
  • For U(1)_{B-L} and U(1)_{Le-Lmu} models, the presence of invisible neutrino decays reduces the projected reach by an O(1) factor and limits the mass reach to about 100 MeV for B-L.
  • If no signal is found, MUonE will set new exclusion limits that complement upcoming searches at other fixed-target and collider experiments.
  • The search strategy is model-agnostic and could be applied to any long-lived particle that decays to charged tracks inside the first tracking station.

Where Pith is reading between the lines

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

  • The zero-background assumption is the main load-bearing premise; a dedicated background study for the nuclear channel, which can produce K0, Lambda, and charged pions at 54 GeV center-of-mass energy, could shift the projected reach upward if any events pass the three-track displaced-vertex selection.
  • The paper notes a factor-of-8 discrepancy between its simulation and an analytic approximation for the production cross-section; measuring or recomputing that rate on beryllium at 160 GeV would settle the absolute normalization of the search.
  • The same displaced-vertex trigger could be extended to other light, feebly coupled particles such as axion-like particles or scalars that decay to charged lepton pairs, making MUonE a general-purpose long-lived particle facility at a muon beam.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. This paper studies the sensitivity of the upcoming MUonE experiment to long-lived U(1) vector bosons — the kinetic-mixing dark photon, U(1)_{B-L}, and U(1)_{L_e-L_μ} — produced via elastic μe and μN scattering, with displaced decays to e+e-. The authors simulate signal events with MadGraph, weight the μN channel with the Tsai nuclear form factor, apply a cut-based selection (Table 2), and assume zero SM background following Ref. [33]. They present 95% CL exclusion projections for each model and show that adding the μN channel raises the mass reach from ~70 MeV (μe only) to ~100–150 MeV, filling a gap in existing constraints.

Significance. The central claim is physically well motivated and the analysis is transparent: the production channels are separated, the decay is handled by explicit boosts, the visible branching ratios are correctly computed, and the existing constraints are recast with DarkCast. The inclusion of μN scattering is a genuine extension of Ref. [33], and the ~factor-two gain in mass reach is a useful result for the MUonE program. The projected sensitivity to couplings ~1e-5 in the 2–150 MeV window would be an important input to the design of the experiment's new-physics program. However, the reach curves are conditional on two assumptions that are not fully established in the manuscript: zero background in the nuclear channel and the absolute normalization of the μN cross section. These do not invalidate the idea, but they need to be addressed before the curves can be taken as quantitative projections.

major comments (2)
  1. [Sec. 3.4 / Table 2 / Figs. 7–9] The zero-background assumption is load-bearing. Sec. 3.4 states 'we assume the backgrounds are zero in our statistics,' citing Ref. [33], but Ref. [33] simulated backgrounds only for μe→μeA'. The μN channel has √s≈54 GeV and a much larger hadronic event rate (K0→π+π−, Λ→pπ−, etc.). Table 2's caption refers to a 'Supplemental Material' for the background discussion, but no such material is present in the submission. Since the 95% CL curves are computed with N_bkg=0, a surviving background of even a few events directly shifts the coupling reach. A dedicated μN background simulation (or a quantitative analytic estimate of rejection rates in the nuclear environment) is needed before the central 'fill the gap' claim is credible.
  2. [Sec. 3.3] The factor ~8 discrepancy with the improved WW cross section of Ref. [61] is acknowledged but not resolved. Because N_sig ∝ σ in Eq. (4.1), and the 95% CL limit has g^2 ∝ 1/σ, an 8-fold cross-section uncertainty translates into a factor ~2.8 shift in the coupling reach shown in Figs. 7–9. The authors attribute the discrepancy to m_beam ≪ m_A' failing for muons, but the manuscript does not validate the MadGraph+form-factor procedure in the regime where most high-mass signal events lie. At minimum, a comparison of the generated inclusive distributions with the analytic calculation, or a systematic study of the form-factor cut t < m_p^2/2, is needed to establish that the projected μN reach is not dominated by a normalization artifact.
minor comments (3)
  1. [Fig. 4] The axis labels appear as '10□2 10□1' in the provided version; please fix the exponent rendering so the mass axis is legible.
  2. [Sec. 4.3] The U(1)_{L_e-L_μ} model is referred to as U(1)_{Lμ-Le} at the start of Sec. 4.3; please harmonize the notation with Table 1.
  3. [Eq. (4.1)] The factor 8 in the luminosity is explained by the last-5-modules choice, but the factor 4 for the nuclear luminosity from the Be atomic number deserves a one-line derivation; as written it is easy to misread as per-nucleus rather than per-electron normalization.

Circularity Check

1 steps flagged

μN sensitivity curves depend on a self-cited zero-background assumption imported from a μe-only study.

specific steps
  1. self citation load bearing [Sec. 3.4 (Backgrounds); applied in Sec. 4, Figs. 7–9]
    "Ref. [33] performed a systematic, simulation-based analysis for the background process with an inclusive fourth track. It was concluded that the backgrounds can all be safely rejected. ... As a conclusion, all backgrounds can be safely rejected by our search strategy, and we assume the backgrounds are zero in our statistics."

    The paper's μN-channel sensitivity curves are computed 'assuming zero background,' but that zero-background conclusion is not derived for μN→μNV. It is imported from Ref. [33], which simulated backgrounds only for μe→μeA′ and shares co-author I. R. Wang with this paper. Since the μN channel operates at √s=54 GeV and involves different hadronic final states, the low-coupling reach—the central 'fill the gap' claim—is effectively an input assumption from a self-citation rather than an independently computed prediction. The signal simulation and mass reach are otherwise self-contained.

full rationale

The paper's headline result—that MUonE can probe vector-boson masses up to ~100–150 MeV—is not itself fitted or definitionally circular: the production cross sections are generated with MadGraph, the decay widths are standard, and the signal acceptances are computed event-by-event with the Table 2 cuts. No fitted parameter is renamed as a prediction. The single circularity-adjacent element is the zero-background assumption for the new μN channel. Section 3.4 adopts the conclusion of Ref. [33]—a prior study with overlapping authorship—that all backgrounds can be safely rejected, even though Ref. [33] simulated only μe→μeA′ backgrounds and did not address μN scattering at √s=54 GeV. The 95% CL contours in Figs. 7–9 are then derived assuming zero background, so the low-coupling boundary of the excluded region is an inherited assumption rather than a computed result. This is a load-bearing self-citation, but it does not eliminate the independent content of the signal simulation and the kinematic argument for the enhanced mass reach. Accordingly, the circularity score is 4 rather than higher.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 3 invented entities

The paper is a sensitivity projection: the three model couplings (ε, g_B−L, g_eμ) are scanned over logarithmic grids, not fitted, so the model parameters are not free parameters in the fitting sense. The four hand-chosen analysis choices listed above directly shape the reach curves. No new entities are postulated; the three mediators are established benchmark models from the cited literature, each with external falsifiable handles. The main inherited assumption is the zero-background claim from Ref [33].

free parameters (4)
  • Daughter energy threshold (1 GeV)
    Table 2; hand-chosen mimic of detector response; directly sets the minimum detectable vector-boson energy (~2 GeV) and suppresses low-mass μe-produced signal.
  • Decay-volume window (25-140 mm)
    Eq. (3.1); derived from the 10δz displacement requirement with δz ≈ 1 mm; hand-chosen factor of 10.
  • Last-5-modules luminosity restriction = factor 1/8 on L
    Sec. 3.2; assumes all but the last five modules are unusable for PID; suppresses L_e and L_N by 8 and substantially reduces the projected reach.
  • Per-particle fake rate threshold (1.6%) = 1.6%
    Sec. 3.4; inherited from Ref [33]; threshold below which the ~4000 K0/Λ background events can be rejected by the ECAL.
axioms (6)
  • domain assumption The vector bosons decay only to SM products (no lighter dark-sector states).
    Sec. 2 and Sec. 4: 'all of our searches are based on the assumption that the vector bosons only decay back to SM particles.' If invisible dark-sector decays dominate, the displaced e+e- search does not apply.
  • domain assumption SM backgrounds at MUonE can be reduced to zero by the stated cuts, inherited from Ref [33].
    Sec. 3.4; Ref [33] simulated backgrounds for μe scattering only; the same conclusion is assumed for the μN channel, which has higher CoM energy and can produce hadronic tracks.
  • standard math The nuclear form factor G2(t) parameterization (Eqs. 3.2-3.3) is valid for t << m_p^2.
    Sec. 3.3; events with t > m_p^2/2 are discarded; standard literature parameterization from Refs [55,56].
  • domain assumption U(1)_{B−L} anomaly cancellation requires heavy right-handed Majorana neutrinos; U(1)_{L_e−L_μ} is anomaly-free in the SM.
    Sec. 2; standard model-extension assumptions cited to Refs [9,10,6-8].
  • domain assumption Tree-level MadGraph cross sections with form-factor weighting accurately capture μN → μN V and μe → μe V production.
    Sec. 3.3; the factor-8 discrepancy with Ref [61]'s improved-WW technique is attributed to the invalid m_beam << m_A' assumption. If the MadGraph calculation is wrong, the reach changes by up to sqrt(8).
  • ad hoc to paper Assumed detector geometry: 3rd tracking station at 1 m from target, 2nd midway; ECAL behavior and PID fake rates as needed for background rejection.
    Sec. 3.1-3.2; station positions 'have not been precisely determined yet'; the decay-volume definition and background-rejection argument depend on these placements.
invented entities (3)
  • Dark photon A' (kinetic-mixing U(1)_D mediator) independent evidence
    purpose: Benchmark model defining the ε vs m_A' plane MUonE would constrain via displaced e+e- decays.
    Not introduced by this paper; standard model from Okun 1982 / Holdom 1986 with extensive existing constraints; the displaced e+e- decay is an external falsifiable handle.
  • U(1)_{B−L} gauge boson Z'_B−L independent evidence
    purpose: Second benchmark; couples to all SM fermions; tests the impact of an additional invisible νν decay channel on the reach.
    Prior-literature model (Marshak & Mohapatra 1980); independently constrained by Borexino, CHARM-II, and beam-dump experiments.
  • U(1)_{L_e−L_μ} gauge boson Z'_eμ independent evidence
    purpose: Third benchmark; electron/muon-flavored mediator with distinctive interference behavior in μe scattering.
    Prior-literature model (Foot 1991; He et al. 1991); constrained by neutrino-electron scattering and Super-K oscillation probes.

pith-pipeline@v1.3.0-alltime-deepseek · 15272 in / 24489 out tokens · 212257 ms · 2026-08-03T23:59:54.524251+00:00 · methodology

0 comments
read the original abstract

The upcoming MUonE experiment aims to precisely measure the running of the fine structure constant via elastic muon-electron scattering, to shed light on the current tension in the muon's anomalous magnetic moment. In addition to its primary function as a precision experiment, MUonE also offers a unique testing ground to probe long-lived vector bosons. Such vector bosons can be produced via $\mu e \to \mu e V$ or $\mu N \to \mu N V$ scattering and decay into an electron/positron pair a few centimeters away from the interaction point. With its high-resolution tracking system and unique geometric design, MUonE is well-suited to reconstruct displaced vertices close to the target, allowing it to probe parameter space previously unattainable at colliders and longer-baseline beam dump experiments. We present a comprehensive study of the discovery potential of BSM vector boson mediators at the MUonE experiment. We show that MUonE can fill the long-standing gap in the parameter space of vector boson mediators with masses up to around 100 MeV.

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