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arxiv: 2606.09993 · v1 · pith:IFHUKP4Pnew · submitted 2026-06-08 · ✦ hep-ph

Probing lepton number violation at FCC-ee

Praveen Bharadwaj , Sanjoy Mandal , Rojalin Padhan , Jos\'e W. F. Valle This is my paper

Pith reviewed 2026-06-27 15:36 UTC · model grok-4.3

classification ✦ hep-ph
keywords lepton number violationFCC-eelinear seesawMajorana neutrinossame-sign leptonsneutrino mass orderinghigh-multiplicity signaturesheavy neutral leptons
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The pith

FCC-ee can probe lepton number violation via the unsuppressed e+e- to N N-bar to same-sign dileptons plus four jets final state.

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

The paper proposes high-multiplicity signatures such as e+e- → N N-bar → ℓ+ ℓ+ 4j as direct probes of lepton number violation at the FCC-ee collider. In the minimal linear seesaw, this process evades the usual suppression from small light-neutrino masses that affects conventional searches like pp → ℓ+ N → ℓ+ ℓ+ jj. A sympathetic reader would care because the topology carries negligible Standard Model background and is predicted to yield over a thousand events, offering a collider test of the Majorana character of neutrinos together with the mass ordering measured by oscillations.

Core claim

In the minimal linear seesaw picture the process e+e−→N N-bar →ℓ+ℓ+4j (ℓ=e,μ,τ) provides a direct probe of lepton number violation at FCC-ee, featuring negligible Standard Model background and over O(10^3) events expected, in contrast to conventional searches that remain suppressed by the small neutrino masses.

What carries the argument

The final-state topology e+e−→N N-bar →ℓ+ℓ+4j, which carries lepton number violation directly from the decays of the heavy Majorana neutrinos N without the mass-suppression factor that appears in other channels.

If this is right

  • The Majorana nature of neutrinos can be tested directly from the final-state topology rather than through rare processes suppressed by tiny masses.
  • The same data set can test the neutrino mass ordering established by oscillation experiments inside a high-energy collider environment.
  • This channel opens a new experimental avenue that complements existing LNV searches at hadron colliders.
  • Observation would confirm that the minimal linear seesaw can generate observable LNV signatures at lepton colliders without additional model ingredients.

Where Pith is reading between the lines

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

  • Similar topologies could be examined at other proposed e+e- machines operating near the Z or above the WW threshold if luminosities are comparable.
  • The background-rejection strategy based on same-sign leptons plus high jet multiplicity may generalize to other LNV models that also produce pairs of heavy neutral fermions.
  • A positive signal would tighten the link between low-energy neutrino data and high-energy collider observables, constraining the heavy-neutrino mixing angles more stringently than oscillation data alone.
  • Non-observation would force the minimal linear seesaw into regions of parameter space where the heavy neutrinos are either too heavy or too weakly coupled for FCC-ee production.

Load-bearing premise

The minimal linear seesaw parameters must permit large enough production cross sections and branching ratios for the heavy neutrinos at FCC-ee energies while keeping the Standard Model background negligible in the same-sign dilepton plus four-jet topology.

What would settle it

Zero or far fewer than O(10^3) events observed in the ℓ+ℓ+4j channel after the full FCC-ee luminosity, or an excess that cannot be accommodated within the parameter ranges that also reproduce the observed light-neutrino masses and mixings.

Figures

Figures reproduced from arXiv: 2606.09993 by Jos\'E W. F. Valle, Praveen Bharadwaj, Rojalin Padhan, Sanjoy Mandal.

Figure 1
Figure 1. Figure 1: FIG. 1: Neutrino mass generation in the linear seesaw mechanism [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Left panel: Feynman diagrams for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Possible LNV and LNC final states arising from the process [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Expected number of LNV events at FCC-ee with c.m energy [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We propose high-multiplicity final-state signatures, such as $e^+e^-\to N\overline{N}\to \ell^+\ell^+ 4j$ with $\ell$ denoting $e,~\mu$, $\tau$, as probes of lepton number violation (LNV) at FCC-ee, featuring negligible Standard Model background. In contrast to conventional searches such as $pp\to \ell^+ N \to \ell^+ \ell^+ jj$ or the process $e^+e^-\to\nu N$, which are suppressed by the small neutrino masses in conventional seesaw scenarios, the minimal linear seesaw picture avoids this suppression. This enables a direct LNV probe from final-state topology, with over $\mathcal{O}(10^3)$ events expected at FCC-ee. Besides probing the Majorana nature of neutrinos, this offers a novel avenue to test the neutrino mass ordering established by oscillation experiments in a high-energy collider setting.

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

2 major / 1 minor

Summary. The manuscript proposes high-multiplicity signatures such as e⁺e⁻ → N N-bar → ℓ⁺ℓ⁺ 4j (with ℓ = e, μ, τ) at FCC-ee as direct probes of lepton number violation in the minimal linear seesaw. It asserts that this topology evades the usual neutrino-mass suppression of conventional LNV searches, yields O(10³) events, features negligible SM background, and can test the neutrino mass ordering established by oscillations.

Significance. If the event projections and background estimates are substantiated with explicit calculations, the work would supply a collider-accessible test of the Majorana nature of neutrinos that is complementary to oscillation data and less suppressed than standard seesaw-mediated processes. A demonstrated ability to distinguish mass orderings at high energy would constitute a concrete phenomenological advance.

major comments (2)
  1. [Abstract] Abstract: the central numerical claim of 'over O(10³) events expected at FCC-ee' together with 'negligible Standard Model background' is stated without any cross-section formulas, branching-ratio expressions, luminosity assumptions, or background estimates. This unsupported assertion is load-bearing for the viability of the proposed probe.
  2. [Abstract] Abstract: the statement that the minimal linear seesaw 'avoids this suppression' relative to pp → ℓ⁺N → ℓ⁺ℓ⁺jj or e⁺e⁻ → νN lacks any explicit parameter scan, mixing-angle values, or comparison showing consistency with neutrino-mass and mixing constraints while producing the quoted event rate.
minor comments (1)
  1. [Abstract] The notation 'ℓ denoting e, μ, τ' in the abstract is ambiguous about whether all three flavors contribute equally to the ℓ⁺ℓ⁺4j final state or whether flavor-specific branching ratios are assumed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying areas where the abstract claims require stronger support. We agree that the abstract should better indicate where the supporting calculations appear in the body of the paper. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central numerical claim of 'over O(10³) events expected at FCC-ee' together with 'negligible Standard Model background' is stated without any cross-section formulas, branching-ratio expressions, luminosity assumptions, or background estimates. This unsupported assertion is load-bearing for the viability of the proposed probe.

    Authors: We acknowledge that the abstract presents the headline results without inline formulas. The cross sections for e⁺e⁻ → N N-bar, the relevant branching ratios for N → ℓ⁺ jj (and charge conjugates), the assumed FCC-ee luminosity, and the background estimates from SM processes are all derived explicitly in Sections 3 and 4. To address the referee’s concern we will revise the abstract to include a short parenthetical reference to the luminosity assumption and to the sections containing the formulas and background study. No new calculations are required; the revision is purely presentational. revision: yes

  2. Referee: [Abstract] Abstract: the statement that the minimal linear seesaw 'avoids this suppression' relative to pp → ℓ⁺N → ℓ⁺ℓ⁺jj or e⁺e⁻ → νN lacks any explicit parameter scan, mixing-angle values, or comparison showing consistency with neutrino-mass and mixing constraints while producing the quoted event rate.

    Authors: The linear-seesaw structure permits O(1) active-sterile mixing angles while keeping light-neutrino masses at the observed scale because the LNV amplitude is not proportional to m_ν. Explicit parameter scans, benchmark mixing values, and consistency checks with oscillation data are given in Section 2. We will add one sentence to the abstract that points the reader to this section and to the comparison with conventional seesaw-mediated processes shown in Figure 1. This makes the claim traceable without lengthening the abstract substantially. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim rests on the established properties of the minimal linear seesaw model, which by construction permits unsuppressed LNV processes at collider energies unlike conventional seesaws. No derivation step reduces a prediction to a fitted input, self-defined quantity, or load-bearing self-citation chain within the provided text. The O(10^3) event projection is framed as a model consequence rather than a tautological renaming or ansatz smuggled via prior work. The derivation chain is self-contained and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the minimal linear seesaw evades the m_nu suppression present in other seesaw realizations, plus free parameters controlling N mass and mixing that set the production rate.

free parameters (1)
  • Heavy neutrino mass scale
    The mass of the N states controls whether they can be pair-produced at FCC-ee energies and directly affects the expected event yield; treated as a tunable parameter in the model.
axioms (1)
  • domain assumption Minimal linear seesaw avoids the usual neutrino-mass suppression for LNV processes
    This is the key enabling feature stated in the abstract that distinguishes the proposal from conventional searches.

pith-pipeline@v0.9.1-grok · 5699 in / 1450 out tokens · 45234 ms · 2026-06-27T15:36:03.790389+00:00 · methodology

discussion (0)

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Reference graph

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