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REVIEW 2 major objections 5 minor 67 references

Neutrino t-channels at Colliders: When Light Neutrinos Matter

T0 review · 2 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Light neutrinos, included coherently with heavy neutrinos in seesaw t-channel amplitudes, cancel the lepton-number-violating WW→ℓℓ signal and make lepton-flavor-violating eµjj the promising LHC probe.

desk verdict The theory is the real result: the seesaw GIM-type cancellation kills LNV t-channels and the LNC LFV channel is worth studying, but the LHC eµjj projection is a simplified illustration that is already overtaken by µ→eγ bounds, so treat the numerical reach as indicative, not definitive. read the letter →

arxiv 2607.19461 v1 pith:QIBFUOPF submitted 2026-07-21 hep-ph hep-ex

Claudia Garcia-Garcia , Manuel González-López , Xabier Marcano , Daniel Naredo-Tuero This is my paper · ORCID
classification hep-phhep-ex
keywords heavyneutralleptonstype-Iseesawt-channelscatteringvectorbosonleptonnumberviolationflavorneutrinonon-unitarityLHC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that HNL t-channel searches at colliders are only meaningful when every neutrino in the seesaw spectrum—light and heavy—enters coherently, and that doing so reverses a common expectation. For the lepton-number-violating process W+W+→ℓ+ℓ+, the full amplitude is proportional to Σ_i U_αi U_βi m_i/(t−m_i²), which in the high-energy limit reduces to Σ_i U_αi U_βi m_i = 0; the light neutrinos cancel the heavy ones, so same-sign WW scattering cannot probe type-I seesaw HNLs in the regime where the HNLs are lighter than the collision energy. For lepton-number-conserving but lepton-flavor-violating W+W−→ℓα+ℓβ−, the same coherent sum enforces unitarity and leaves an observable signal controlled by the non-unitarity matrix η. Simulating pp→e±µ∓ jj with VBS kinematics and low missing transverse energy, the paper finds the LHC can exclude |V_eN V*_µN| around 10⁻²–10⁻¹ for m_N ≳ 1 TeV, beating resonant same-sign searches above about 800 GeV. If correct, this shifts the LHC search strategy for TeV-scale HNLs from same-sign dileptons to opposite-sign, different-flavor leptons plus two forward jets.

What carries the argument

The central object is the coherent sum over all neutrino mass eigenstates exchanged in the t-channel, together with two exact relations: Σ_i U_αi U*_βi = δ_αβ for lepton-number-conserving amplitudes, and Σ_i U_αi m_i U_βi = 0 for lepton-number-violating ones. The second, a direct consequence of the zero (1,1) entry in the type-I seesaw mass matrix, turns the LNV amplitude into a vanishing sum once every HNL is lighter than the collision energy. In the LNC LFV case the same machinery produces the effective non-unitarity parameter η_αβ = (1/2) Σ_i V_αi V*_βi, which controls both the high-energy growth of the WW→ℓαℓβ cross section and its eventual unitarization when HNLs enter. This η_αβ is the

What would settle it

Measure the same-sign WW→e±µ± cross section at the LHC at subprocess energies well above the HNL mass: the seesaw framework predicts the light-neutrino contribution cancels the HNL contribution, leaving a rate at the level of the active-neutrino-only term, whereas a rate matching the HNL-only calculation would falsify the central claim. A second, complementary check is the energy dependence of WW→e±µ∓: the paper predicts a unitarity-restoring turnover at √s ≈ m_N, so measuring the cross section on both sides of the HNL mass would discriminate.

Watch

Extended reading notes

Core claim

The paper's central discovery is a destructive-interference cancellation in the type-I seesaw: the complete t-channel amplitude for lepton-number-violating W±W±→ℓ±ℓ± is proportional to Σ_i U_αi U_βi m_i/(t−m_i²), and when all heavy neutrinos are lighter than the collision energy this reduces to Σ_i U_αi U_βi m_i, which vanishes identically by the seesaw relation following from the zero (1,1) block of the neutrino mass matrix. The light neutrinos, far from negligible, are exactly what restores unitary high-energy behavior and kills the LNV signal. For lepton-number-conserving but lepton-flavor-violating W+W−→ℓα+ℓβ−, the same coherent sum reconstructs the unitarity of the mixing matrix; in the

Load-bearing premise

The entire cancellation argument rests on the type-I seesaw mass matrix having a strictly zero (1,1) block and an exactly unitary full (3+n)×(3+n) mixing matrix; the LHC reach estimate additionally assumes the ttbar and VVjj backgrounds dominate with a 20% systematic uncertainty.

Editorial extensions

If this is right

  • LNV same-sign WW-scattering searches, as previously proposed and run, are not sensitive to type-I seesaw HNLs in the regime where m_N² ≪ s; the signal they target is suppressed by the seesaw cancellation.
  • The LHC eµjj channel with VBS kinematics and low missing transverse energy is a promising LFV search: at Run 2, Run 3, and HL-LHC it can reach |V_eN V*_µN| ~ 10⁻²–10⁻¹ for m_N in the TeV range, improving on resonant same-sign searches for m_N ≳ 800–1000 GeV.
  • The search is sensitive to both Dirac and Majorana HNLs, and especially to low-scale seesaw scenarios with pseudo-Dirac HNLs that suppress LNV while allowing sizable active–sterile mixing.
  • When HNLs are too heavy to be produced, the LFV t-channel measurement effectively probes the dimension-6 operator obtained by integrating them out, with sensitivity to η_eµ ≲ O(10⁻²), though in the plotted region this sits near the perturbative-unitarity boundary.
  • The t-channel bounds depend directly on the product V_αN V*_βN and are free of the single-flavor assumptions that complicate reinterpretation of resonant searches.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the same cancellation argument applies to other LNV t-channel processes at any collider, including ℓ⁻ℓ⁻→W⁻W⁻ at lepton colliders, so the conclusion that LNV t-channels are blind to type-I seesaw HNLs is general, not LHC-specific.
  • Editorial inference: any future observation of same-sign WW→ℓℓ above the seesaw-suppressed prediction would point to physics beyond type-I seesaw, such as a lepton-number-violating term in the mass matrix or a non-unitary mixing matrix.
  • Editorial inference: the eµjj strategy can be extended to τℓjj final states, covering the τ sector of the same non-unitarity matrix with similar VBS-based selection.
  • Editorial inference: at very high m_N the projected reach saturates to the dimension-6 operator sensitivity, so a null result at the HL-LHC would place a complementary—though weaker than current low-energy µ→eγ—bound on lepton-flavor-violating non-unitarity.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper revisits HNL-mediated t-channel processes, specifically WW→ℓℓ scattering, and argues that the light neutrinos of the type-I seesaw cannot be neglected. For lepton-number-violating (LNV) W^+W^+→ℓ^+ℓ^+, the amplitude is proportional to Σ_i U_{αi}U_{βi}m_i/(t−m_i^2) (Eq. 11); in the limit where all HNLs are lighter than the collision energy, the seesaw relation Eq. (8) forces a GIM-like cancellation (Eq. 12), suppressing the LNV signal. For lepton-number-conserving (LNC) but lepton-flavor-violating (LFV) W^+W^-→ℓ_α^+ℓ_β^-, the light and heavy contributions interfere to restore unitarity, and the cross section can be expressed in terms of the non-unitarity parameter η_{αβ} (Eq. 17). The paper then presents a MadGraph5+Pythia8+Delphes simulation of pp→eµjj at the LHC, with VBS-like cuts and a signal region defined by hard leptons, high M_eµ, and low missing energy (Eqs. 21–23), claiming a 95% CL reach of |V_eN V*_µN| ~ 10^{-2}–10^{-1} for m_N ≳ 1 TeV, improving on resonant same-sign dilepton searches above m_N ~ 800 GeV.

Significance. The central theoretical result is solid and important. The derivation of the LNV cancellation follows directly from the zero (1,1) block of the type-I seesaw mass matrix together with exact unitarity of the full mixing matrix; the paper makes this explicit in Eqs. (8), (11), and (12), and correctly identifies that many previous t-channel studies neglected the active-neutrino contribution. The analytic LNC cross section in Eq. (17) has the correct heavy- and light-HNL limits (Eqs. 18 and 19), and the reproduction of the cancellation with MadGraph5 (Fig. 2) is a valuable cross-check. If the LHC projection survives closer scrutiny, the paper would provide a concrete, falsifiable search strategy for low-scale seesaw HNLs in a mass range where resonant searches lose sensitivity. The paper also correctly emphasizes that the reach is free of the flavor-pattern ambiguity that complicates reinterpretation of resonant searches. However, the quantitative LHC claim rests on a simplified background model and an optimistic systematic treatment, and the perturbative-unitarity boundary is not fully integrated into the stated mass reach. These issues affect the paper's central phenomenological conc

major comments (2)
  1. [Sec. 5, Eqs. (21)–(24), Fig. 6] The LHC reach claim is not yet robust against background-modeling uncertainties. Only ttbar and VVjj are simulated; multijet and W+jet fake backgrounds are dismissed in one sentence, and the systematic uncertainty is taken as a flat δ_B=0.2 based on a CMS W+W- measurement that does not cover the fake-enriched eµ high-pT, low-MET regime. Because the signal scales as |η_eµ|^2, the 95% CL reach scales roughly as (n_B/δ_B)^{1/4}; a fake contribution at the 50% level or δ_B=0.4 degrades the reach by a factor ~1.2–1.5, which can move the crossing with the CMS resonant limit from m_N~800 GeV toward or beyond the perturbative-unitarity boundary. The authors should provide a detailed cutflow table, an explicit uncertainty breakdown, and either a realistic fake estimate or an explicit caveat that the claimed improvement over resonant searches assumes negligible fakes and δ_B=0.2.
  2. [Sec. 5, Fig. 6 and footnote 9] The paper presents the LFV t-channel as extending LHC sensitivity to HNL masses between 1 and 10 TeV, but it simultaneously states that the horizontal asymptotes of the sensitivity curves lie inside the non-perturbative region, and footnote 9 notes that Γ_N ~ V^2 m_N^3 becomes comparable to m_N in the large-coupling region. Since the main phenomenological conclusion is the improvement over resonant searches for m_N≳800 GeV, the authors must state explicitly whether the claimed exclusion region—and especially the crossing point—lies inside the gray shaded unitarity-violating area. If part of the claimed reach is excluded by tree-level unitarity, the stated mass range and the figure should be restricted or clearly marked accordingly, and the text should not claim a 1–10 TeV reach without that qualification.
minor comments (5)
  1. [Author list] The fourth author's name is typeset as 'Naredo-T uero' in the header; the spacing should be corrected.
  2. [Sec. 5, simulation setup] 'Phythia8' should be 'Pythia8' in the text describing the event-generation chain.
  3. [Fig. 6] The caption of Fig. 6 is missing from the manuscript, and the text refers to a 'right panel' of Fig. 6 without explaining the panel layout. Please add a caption that defines the left and right panels and the meaning of the gray shaded region.
  4. [Sec. 5, CMS reference] In the comparison with the CMS same-sign dilepton search, the text writes 'same-sign e±µ±'; since the signal under study is opposite-sign e±µ∓, please clarify the flavor/charge assignment to avoid confusion.
  5. [Eq. (17)] The expression for σ(W_L^+ W_L^- → ℓ_α^+ ℓ_β^-) is dimensionally consistent and has correct limits, but the prefactor and the logarithmic argument should be double-checked against the exact integration; the m_N^2≪s limit in Eq. (18) follows if log((s+m_N^2)/m_N^2) ≈ log(s/m_N^2), which should be stated explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LNV cancellation and LNC cross section are derived from the seesaw mass matrix and exact unitarity, not fitted; self-citations are non-load-bearing.

full rationale

The paper's central results are self-contained derivations. The LNV suppression follows from the exact relation (Eq. 8), itself a consequence of the zero (1,1) block of the seesaw mass matrix (Eq. 2) and exact diagonalization; Eq. (12) is that relation read at m_N^2 << s. The LNC LFV cross section (Eq. 17) is a calculated amplitude expressed in terms of eta_alpha_beta, with eta defined by eta = (1/2) V V-dagger in Eq. (6); no parameter is fitted to data or to the plotted reach. The MadGraph5 points in Figs. 2 and 3 reproduce the analytic curves using the public UFO model of Ref. [38], which shares an author but is an externally available implementation used as a cross-check, not as the argument establishing the cancellation. Self-citations such as Refs. [18], [22], [30], [38], and [60] are contextual, technical, or benchmark comparisons and are not load-bearing for the main derivation. The main caveats—neglect of multijet/W+jets fakes and the flat delta_B = 0.2 in Eq. (24)—are background-modeling and systematic-risk assumptions, i.e., risks to the LHC projection, not a case of a fitted input being relabeled as a prediction. A possible sign issue in Eq. (16) would be a physics-correctness concern, not circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper adds no invented entities. The central derivation relies on the standard type-I seesaw mass structure and exact unitarity of the extended mixing matrix; the LHC reach additionally rests on simplified detector/systematics assumptions. The model parameters m_N and mixings are scanned, not fitted to data.

free parameters (5)
  • m_N = scanned, e.g. 1-50 TeV in Fig. 6
    HNL mass; the variable being probed, not fitted to data.
  • |V_eN V*_µN| = benchmark 0.2; scanned in Fig. 6
    Central BSM coupling controlling the eµ LFV signal; not fitted.
  • m_ν = 0 for LNC; V^2 m_N for the one-HNL LNV illustration
    Light neutrino mass is set by hand depending on the scenario; affects the cancellation plot in Fig. 2.
  • δ_B = 0.2
    Background uncertainty chosen based on a CMS WW measurement; directly controls the significance and limits.
  • Signal-region cuts = p_Tℓ1>300 GeV, p_Tℓ2>250 GeV, M_eµ>600 GeV, MET<30 GeV
    Chosen by hand after inspecting distributions; a different choice would change the projected reach.
assumptions (5)
  • domain assumption Type-I seesaw mass matrix with vanishing (1,1) block (Eq. 2)
    Defines the model; the cancellation Eq. (8) follows from this zero entry.
  • standard math Exact unitarity of the full (3+n)-dimensional neutrino mixing matrix (Eq. 7)
    Needed for the GIM-like sum and for expressing heavy HNL contributions as -2η.
  • domain assumption Longitudinal W boson scattering dominates the high-energy VBS amplitude
    Used to derive Eq. (17); valid at energies well above m_W.
  • ad hoc to paper Simplified one-HNL / degenerate HNL scenario with m_ν=0 for LNC
    Not the full neutrino mass spectrum; chosen to isolate the eµ LFV t-channel.
  • domain assumption Perturbative unitarity bound from partial-wave analysis up to 14 TeV
    Defines the gray excluded region in Fig. 6; standard tree-level unitarity criterion.

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Pith. "Pith review of Neutrino t-channels at Colliders: When Light Neutrinos Matter." pith.science (2026). https://pith.science/paper/QIBFUOPF

@misc{pith2026260719461,
  author       = {Pith},
  title        = {Pith review of: Neutrino t-channels at Colliders: When Light Neutrinos Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QIBFUOPF}},
  note         = {Machine review of arXiv:2607.19461}
}
abstract

Heavy Neutral Lepton (HNL)-mediated t-channel processes provide a unique opportunity to probe mass scales beyond the kinematic reach of direct production at high-energy colliders. We revisit these processes using the vector boson scattering channel $WW\to\ell\ell$ at the LHC as a case study, highlighting the essential role of the light neutrinos in restoring the proper high-energy unitary behavior of the scattering amplitude. Their inclusion, overlooked in some previous studies, leads to destructive interference that strongly suppresses lepton number violating signatures, demonstrating that a consistent treatment of the full seesaw spectrum qualitatively alters the phenomenology of t-channel HNL searches. This motivates the exploration of lepton number conserving but lepton flavor violating final states instead. We present a detailed analysis of the $pp\to e\mu jj$ channel and show that it provides a promising probe of TeV-scale HNLs in low-scale seesaw scenarios with sizable active-sterile mixing, extending the LHC sensitivity beyond existing direct searches.

Figures

Figures reproduced from arXiv: 2607.19461 by the authors.

Figure 1
Figure 1. HNLs in s- (left) and t- (right) diagrams at a proton-proton collider. Leptonic lines [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. LNV W+W+ → ℓ +ℓ + process in a simplified scenario with one light neutrino ν and one HNL, whose contributions are displayed separately (dashed lines) to show their cancellation when computing the total contribution (solid line). A cut on |ηℓ | < 5 has been imposed to avoid numerical instabilities in the integration. Lines are obtained analytically, while dots show how our treatment with MadGraph5 is able to reproduc… view at source ↗
Figure 3
Figure 3. LFV W+W− → ℓ + α ℓ − β process in a type-I seesaw with degenerate HNLs. Left panel is analogous to that of fig. 2, with the same notation. The right panel shows the total cross section for different values of the HNL masses. The shadowed blue region indicates the high-energy region outside the LHC reach, only for illustration purposes, roughly estimated to (subprocess) energies of 7 TeV. In the heavy HNL limit, they… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Distributions of a representative signal benchmark and cumulative background [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Distributions of a representative signal benchmark and total background events as [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: 95% CL exclusion limits from the neutrino mediated LFV [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

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