REVIEW 2 major objections 5 minor 67 references
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.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · deepseek-v4-flash
2026-08-01 12:40 UTC pith:QIBFUOPF
load-bearing objection 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. the 2 major comments →
Neutrino t-channels at Colliders: When Light Neutrinos Matter
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
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
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
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.
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.
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.
Where Pith is reading between the lines
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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)
- [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.
- [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)
- [Author list] The fourth author's name is typeset as 'Naredo-T uero' in the header; the spacing should be corrected.
- [Sec. 5, simulation setup] 'Phythia8' should be 'Pythia8' in the text describing the event-generation chain.
- [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.
- [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.
- [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
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.
Axiom & Free-Parameter Ledger
free parameters (5)
- m_N =
scanned, e.g. 1-50 TeV in Fig. 6
- |V_eN V*_µN| =
benchmark 0.2; scanned in Fig. 6
- m_ν =
0 for LNC; V^2 m_N for the one-HNL LNV illustration
- δ_B =
0.2
- Signal-region cuts =
p_Tℓ1>300 GeV, p_Tℓ2>250 GeV, M_eµ>600 GeV, MET<30 GeV
axioms (5)
- domain assumption Type-I seesaw mass matrix with vanishing (1,1) block (Eq. 2)
- standard math Exact unitarity of the full (3+n)-dimensional neutrino mixing matrix (Eq. 7)
- domain assumption Longitudinal W boson scattering dominates the high-energy VBS amplitude
- ad hoc to paper Simplified one-HNL / degenerate HNL scenario with m_ν=0 for LNC
- domain assumption Perturbative unitarity bound from partial-wave analysis up to 14 TeV
read the original 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
Reference graph
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