{"id":"bc7c15af-3e61-4010-8100-edd62da434c9","arxiv_id":"2607.19461","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The same-sign WW→ℓℓ t-channel signal for heavy Majorana neutrinos is cancelled by light-neutrino contributions in the seesaw model; the opposite-sign eµjj channel is a better probe.","lead":"This paper shows that in the seesaw model, the light neutrinos cancel the lepton-number-violating collider signal usually used to hunt for heavy neutrinos, so that signal disappears. It proposes instead a lepton-flavor-violating final state (e and mu with two jets) at the LHC, which could probe heavy neutrinos above the TeV scale.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The LHC reach claim rests on an optimistic background model: fakes are neglected and δ_B=0.2 is assumed; a larger fake component or systematic could erase the m_N≥1 TeV advantage over resonant searches.","rationale":"The reader's CONDITIONAL verdict is appropriate, and the weakest assumption is the LHC background projection. My stress-test confirms that the theoretical cancellation is solid within the type-I seesaw: Eq. (8) is exact, the factorization in Eq. (11) is valid, and the residual after cancellation is parametrically suppressed by m_i^2/|t| when m_N^2<<s. The UV-completion caveat raised in the reader's weakest_assumption is a scope limitation, not an internal inconsistency, because the paper explicitly frames its conclusion as type-I seesaw. However, the quantitative claim that the LFV t-channel surpasses resonant searches for m_N≳800 GeV depends on n_B and δ_B, which are neither tabulated nor robustly estimated. A fake background or larger systematic uncertainty could shift the reach by a factor comparable to the gap between the t-channel and resonant curves. The reader already flagged this, so no verdict change is needed; the paper should be published conditional on a more detailed experimental background study and public cutflows.","tokens_in":17035,"tokens_out":12995,"duration_ms":137599,"concrete_test":"Reproduce Fig. 6 after adding a fake background estimate derived from a same-sign e±µ± control region (or from ATLAS/CMS fake-factor tables) with the VBS and lepton pT cuts, and with δ_B=0.4. Evaluate whether the 95% CL curve still excludes |V_eN V*_µN| below the CMS resonant limit for m_N=1, 2, 3 TeV. If the crossing moves to m_N>2 TeV or the curve enters the non-perturbative region, the paper's central phenomenological conclusion is weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical result—the GIM-like cancellation in Eq. (8)/(12) for type-I seesaw LNV t-channels—is internally consistent and not the weak point: Eq. (8) follows from the zero (1,1) block of the mass matrix and exact unitarity, and the paper demonstrates the cancellation with MG5. The load-bearing concern is the quantitative LHC claim in Sec. 5/Fig. 6. The signal region (Eq. 23) is defined by very hard leptons (pT>300/250 GeV), M_eµ>600 GeV and ETmiss<30 GeV. The only backgrounds simulated are ttbar and VVjj; multijet/W+jets fakes are asserted to be data-driven and neglected. The significance uses Eq. (24) with a flat δ_B=0.2, justified by a CMS W+W- measurement that does not include the fake-enriched eµ regime. Because the signal scales as |η_eµ|^2, the 95% CL reach scales roughly as (n_B/δ_B)^{1/4}; if fakes contribute 50% of n_B or the systematic uncertainty is 40% rather than 20%, the reach in |V_eN V*_µN| degrades by a factor ~1.2–1.5. This could move the crossing with the CMS resonant limit from m_N~800 GeV to above the perturbative-unitarity boundary. Without a cutflow table or an uncertainty breakdown, the 'improvement over resonant searches' is not secure.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":17364,"tokens_out":3769,"duration_ms":38637,"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":[{"comment":"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.","section":"Sec. 5, Eqs. (21)–(24), Fig. 6"},{"comment":"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.","section":"Sec. 5, Fig. 6 and footnote 9"}],"minor_comments":[{"comment":"The fourth author's name is typeset as 'Naredo-T uero' in the header; the spacing should be corrected.","section":"Author list"},{"comment":"'Phythia8' should be 'Pythia8' in the text describing the event-generation chain.","section":"Sec. 5, simulation setup"},{"comment":"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.","section":"Fig. 6"},{"comment":"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.","section":"Sec. 5, CMS reference"},{"comment":"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.","section":"Eq. (17)"}],"recommendation":"major_revision","confidential_remarks":"The theoretical core of this paper is sound and likely worth publishing. The main risk is the phenomenological claim in Section 5/Figure 6, which is built on a simplified background model and a flat systematic uncertainty. I do not see a fatal flaw in the analytic derivation, but the LHC reach statement needs to be made conditional on realistic background/systematic assumptions and on the perturbative-unitarity boundary. A major revision with a cutflow table and explicit caveats would be appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know about this paper is that Section 4 is the real contribution. The authors show that in a type-I seesaw, the LNV t-channel amplitude is proportional to Σ_i Uαi Uβi mi/(t − mi²), and once the HNLs are lighter than the available energy, this becomes Σ_i Uαi Uβi mi = 0, a direct consequence of the zero (1,1) block of the mass matrix. The light neutrinos are not a small correction—they cancel the heavy contribution. That is the same mechanism as in neutrinoless double beta decay, and it means previous same-sign WW t-channel search interpretations rested on an inconsistent treatment of the seesaw spectrum. The LNC LFV channel avoids the mass insertion, and the cross section formula in Eq. (17) is derived cleanly, with the correct heavy- and light-mass limits. The logic is internally consistent, and the MadGraph curves reproduce the analytic ones. This is genuine, citable phenomenology.\n\nWhat I am less convinced by is Section 5. The LHC projection is a LO parton-level analysis with Delphes, only ttbar and VVjj backgrounds, fakes asserted to be data-driven and dropped, and one flat 20% systematic. There is no cutflow table, no uncertainty breakdown, no public code. That is not a flaw in the theory, but it means Fig. 6 should be labeled an illustration rather than a search projection. The stress-test concern about fakes and δ_B is fair: the eµ signal region is exactly the regime where fake lepton backgrounds from multijet and W+jets can be non-negligible, and a 20% systematic taken from a CMS WW measurement does not obviously cover that regime. A factor of 1.3–1.5 degradation in reach is plausible.\n\nThe bigger caveat is one the authors themselves state: the eµ channel is already excluded by µ→eγ by several orders of magnitude. They reach |η_eµ| ~ 10⁻², while precision data give ~10⁻⁵. So as a realistic discovery channel, eµjj at the LHC is not going to win. The paper frames this as complementary, which is honest, but it sharply limits the practical significance. The interesting extension is the τℓ channels, where precision bounds are weaker, but that is only mentioned in passing.\n\nWho should read this: anyone doing HNL collider phenomenology, especially people recasting same-sign WW searches. The theoretical point deserves a serious referee. The experimental reach claims need more careful treatment—fake estimates, a cutflow, and an honest discussion of the precision-data gap—before being quoted as projections.\n\nRecommendation: send it to peer review. The theory is solid and important enough; the collider section needs revision but is not a reason to desk reject.","headline":"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.","tokens_in":17928,"tokens_out":3176,"would_cite":true,"duration_ms":34590,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["heavy neutral leptons","type-I seesaw","t-channel scattering","vector boson scattering","lepton number violation","lepton flavor violation","neutrino non-unitarity","LHC"],"falsifier":"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.","tokens_in":16874,"feed_emoji":"⚛️","tokens_out":9492,"duration_ms":83085,"temperature":0.7,"pith_summary":"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.","feed_headline":"Light neutrinos kill LNV t-channel HNL searches at the LHC","feed_subtitle":"A consistent seesaw treatment erases same-sign WW→ℓℓ and makes eµjj the TeV-scale HNL probe.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Light neutrinos erase LNV t-channel signals at LHC","LNV dies as light neutrinos cancel t-channel HNL","Light neutrinos restore unitarity, kill LNV t-channel","Seesaw consistency erases LNV, makes eµjj the probe","Light neutrinos are the LNV killer in t-channels"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Light neutrinos erase LNV t-channel signals at LHC","LNV dies as light neutrinos cancel t-channel HNL","Light neutrinos restore unitarity, kill LNV t-channel","Seesaw consistency erases LNV, makes eµjj the probe","Light neutrinos are the LNV killer in t-channels"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0006,"raw_usage":{"total_tokens":2642,"prompt_tokens":749,"completion_tokens":1893,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":493,"completion_tokens_details":{"reasoning_tokens":1804}},"tokens_in":493,"tokens_out":1893,"duration_ms":12790,"temperature":1.0,"reasoning_tokens":1804,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T12:40:20.305797+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}