{"id":"22c3f952-8ec6-4677-94b2-219968a318c8","arxiv_id":"1908.02302","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A comprehensive frequentist global fit maps the currently allowed mass and mixing space for three right-handed neutrinos between 60 MeV and 500 GeV and finds no significant new physics.","lead":"This paper runs a global frequentist fit of the Standard Model extended by three right-handed neutrinos, combining dozens of collider, beam-dump, precision, and cosmology measurements. It maps which heavy-neutrino masses and mixing strengths remain experimentally allowed up to 500 GeV, and flags small hints in existing data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"DELPHI tau limit used without kinematic suppression could shift U_tau bounds in the 0.5-4 GeV region.","rationale":"The reader's weakest assumption identifies the statistical recasting of direct search limits as the key approximation. I agree, and I sharpen it to a specific, testable sub-case: the DELPHI flavour-independent limit applied to tau couplings below the tau mass threshold. This is the place where a known physical suppression is acknowledged but not implemented, and where the resulting bound is the dominant one for an entire mass range. If the concrete test shows only a small shift, the concern is resolved and the paper's conditional acceptance stands. If the shift is large, the U_tau constraints and the cross-flavour bounds in Figs. 6-7 would need revision, weakening the quantitative part of the central claim. I do not see a more fundamental internal inconsistency: the model setup, the Casas-Ibarra parametrisation, the use of profile likelihoods, and the disclosure of approximate recasting and Wilks-based contours are all coherent, and the paper is transparent about its limitations. The independent support from GAMBIT's public code and the deposited scan data is real, but it validates the implementation, not the fidelity of the recasted limits. The verdict should remain CONDITIONAL, as the reader concluded, because the central argument is supported but the quantitative constraints depend on an approximation that should be validated or quantified before the contour maps are used as precise references.","tokens_in":68646,"tokens_out":6157,"duration_ms":76645,"concrete_test":"Re-derive the DELPHI likelihood with the tau-threshold suppression included: for M_N below about 4 GeV, remove or phase-space suppress tau-containing decay channels in the short- and long-lived signatures, and rescale the quoted U^2 limit by the corresponding partial-width ratio (using the expressions in Sec. B.2). Then recompute the profile likelihood in the M_I-U^2_tau plane for M_I between 0.5 and 4 GeV, for both normal and inverted hierarchy, and compare the 1-sigma and 2-sigma upper edge with Fig. 3. If the edge moves upward by more than about 50%, the quoted U_tau upper bounds in this mass region are not robust and should be replaced by the conservative limit, with consequences for Figs. 6-7 and for the claim of comprehensiveness.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is that the direct-search likelihoods, calibrated to published limits under each experiment's simplified model, correctly represent the model's predictions when profiled over the full Casas-Ibarra parameter space. This is weakest for DELPHI's tau constraint: Sec. 3.3.6 states that the flavour-independent limit is applied to U_tau even though the quoted bounds become weaker for masses below about 4 GeV, and the size of the tau-mass suppression is not quantified. DELPHI is the dominant direct constraint on U_tau for roughly 0.5-80 GeV (Sec. 5.2, Figs. 3 and 36-38), so an overestimate of its sensitivity directly shifts the upper bounds on U^2_tau in Fig. 3 and the cross-flavour products in Figs. 6-7. The paper itself flags this caveat and a related simplified-model caveat in Sec. 3.3.7, but does not estimate the resulting shift in the quoted constraints. The central claim of providing the most comprehensive assessment does not require exact limits, but quantitative upper limits should not rest on an unvalidated extrapolation in a region where one experiment dominates.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a global frequentist analysis of the Standard Model extended by three right-handed Majorana neutrinos with masses between 60 MeV and 500 GeV, using the GAMBIT framework. The parameter space is scanned with the Casas-Ibarra parametrisation, and the authors combine likelihoods for active neutrino oscillations, electroweak precision observables, lepton flavour violation, lepton universality, CKM unitarity, neutrinoless double-beta decay, BBN, and a large set of direct search experiments. The results are presented as profile likelihood maps in the mass-mixing planes for electron, muon, and tau flavour couplings, cross-flavour products, and flavour-mixing triangles as a function of the lightest neutrino mass. The paper also identifies small (around 2 sigma) excesses driven by Gamma_inv, CKM, and R_K, and claims to provide the most comprehensive assessment of this model below the TeV scale so far.","tokens_in":68935,"tokens_out":5443,"duration_ms":68856,"significance":"If the results are correct, the profile likelihood maps in Figs. 1-7 and the flavour-mixing constraints in Figs. 11-13 constitute the most complete global constraints on the three-right-handed-neutrino model in this mass range. The analysis is a substantial technical effort: it uses an open-source framework, provides a new GAMBIT module, publishes the scan data on Zenodo, and explicitly combines many constraints that previous studies treated separately. The paper is commendably transparent about its approximations, including the use of approximate likelihoods calibrated to published limits, the absence of a full sampling-based goodness-of-fit test, and the reliance on Wilks' theorem for contour estimation. The Casas-Ibarra parametrisation builds in neutrino oscillation data as a modelling choice rather than as an external test, which is appropriate for a scan-oriented global fit. The main weakness is that some quantitative upper limits, especially for the tau coupling, rest on a small number of unvalidated recasting assumptions.","major_comments":[{"comment":"The DELPHI tau-flavour limit is applied without quantifying the kinematic suppression from the tau mass below about 4 GeV. The paper itself states that the quoted bounds become weaker in this region, but it then uses the flavour-independent limit as-is for U_tau. Since DELPHI is the dominant direct constraint on U_tau for roughly 0.5-80 GeV, an overestimate of its sensitivity would directly shift the upper bounds on U_tau^2 in Fig. 3 and the cross-flavour products in Figs. 6 and 7. The authors should either implement a conservative tau-mass suppression factor, rerun the fit with a weakened DELPHI likelihood, or quantify the resulting shift in the quoted upper limits.","section":"Sec. 3.3.6, Figs. 3, 6, 7"},{"comment":"The 1 sigma and 2 sigma contours in the profile likelihood plots are estimated using Wilks' theorem with two degrees of freedom, but the likelihood is a composite of approximate Poisson and half-Gaussian likelihoods calibrated to published limits, and the contours are drawn on a capped likelihood. Wilks' theorem may be inaccurate for zero-event Poisson likelihoods, for parameters with physical boundaries at zero coupling, and for composite likelihoods that are not genuine likelihoods of the data. The authors do not provide any Monte Carlo validation or calibration of the profile likelihood ratio. Since the quantitative confidence levels are a central output of the paper, this approximation should be either validated or explicitly softened in the interpretation of the contours.","section":"Sec. 4 and 5.1, Figs. 1-7"},{"comment":"The BBN likelihood is implemented as a step function requiring each RHN lifetime to be less than 0.1 s, and this bound is applied over the whole scanned range, including m_nu0 values as low as 1e-7 eV. The paper acknowledges in Sec. 3.2.6 that the BBN bound can be weakened for m_nu0 below about 1e-3 eV because the RHNs may not thermalise. This could overstate the lower bounds on U_tau^2 shown in Fig. 3 and on U_I^2 in Fig. 4 for small m_nu0. The impact of this caveat on the plotted lower limits should be quantified, or the affected regions should be identified in the figures.","section":"Sec. 3.2.6, Figs. 3 and 4"}],"minor_comments":[{"comment":"The phrase 'three right-handed neutrinos model' appears twice and should read 'three right-handed neutrino model'.","section":"Abstract and Conclusions"},{"comment":"There is a typo: 'indculde' should be 'include'.","section":"Sec. 3.3.10"},{"comment":"There are typos: 'folliders' should be 'colliders' and 'measurments' should be 'measurements'.","section":"Sec. 6"},{"comment":"The text contains 'in strictive' which should be 'instructive'.","section":"Sec. 2.6"},{"comment":"The statement that the paper performs 'the first full frequentist analysis' is somewhat in tension with the later statement that no full sampling-based goodness-of-fit analysis is performed; rewording to 'first full frequentist profile-likelihood analysis' would be more precise.","section":"Sec. 1.2"},{"comment":"The parameter denoted delta_M21 would be clearer as Delta M21, consistent with the text in Sec. A.1, to avoid confusion with the active neutrino mass splitting Delta m^2_21.","section":"Sec. 4.2, Table 6"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically solid and the authors are unusually transparent about limitations. The key risk is the DELPHI tau recasting: because DELPHI dominates the tau coupling constraints in a wide mass range, an unquantified kinematic overestimate could propagate into several headline figures. If the authors provide a conservative treatment or quantify the shift, I would be happy to reconsider. The Wilks-theorem issue and the BBN thermalisation caveat are secondary but should also be addressed, at least by softening the associated quantitative claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is the most complete frequentist global fit of the three-right-handed-neutrino seesaw below the TeV scale, and it mostly delivers on its claims. The new content is real: active neutrino likelihoods included directly in the scan, a broad set of LFV and lepton-universality observables, an improved CKM unitarity treatment, and the first flavour-mixing-pattern constraints as a function of the lightest neutrino mass, including an explicit recovery of the n=2 limit. The GAMBIT implementation and the Zenodo dataset make the results reproducible, which is worth taking seriously.\n\nThe paper is generally careful. The main caveats are all disclosed by the authors. Likelihoods for direct searches are approximate recasts of published limits, using Poisson or half-Gaussian forms calibrated to quoted confidence levels. There is no full sampling-based goodness-of-fit, and the contour levels come from Wilks' theorem. Given the high dimensionality and the use of profile likelihoods, those are reasonable choices, but they are approximations and the paper says so.\n\nThe one place I would push back is the DELPHI treatment for U_tau. The paper applies the flavour-independent DELPHI limit to U_tau even though DELPHI itself says the bound weakens below about 4 GeV, and the tau-mass suppression is not quantified. Since DELPHI is the dominant direct constraint on U_tau between roughly 0.5 and 80 GeV, this could shift the quoted upper bound in the sub-4 GeV region. The authors flag this in Sec. 3.3.6 but do not estimate the effect. That is a genuine soft spot, and it should be fixed in revision by modelling the tau kinematic factor or adding an uncertainty band. It does not overturn the central result—the map is still the best available—but the U_tau contours in that range should be read with a grain of salt.\n\nThe excesses near 2 sigma in Gamma_inv, CKM, and R_K are handled honestly and are not oversold.\n\nWho is this for: phenomenologists planning NA62, DUNE, SHiP, or FCC-ee searches, and anyone who needs a baseline for interpreting future heavy-neutrino results. It deserves peer review. Recommended actions: ask the authors to quantify the DELPHI U_tau suppression, provide an uncertainty estimate for the likelihood recasting, and ideally validate with a second scanner or a coverage check. These are revision-level issues, not grounds for rejection.","headline":"The first full frequentist global fit of the three-right-handed-neutrino seesaw below the TeV scale—solid, careful, and reproducible, with a few disclosed statistical approximations and one unquantified DELPHI caveat that deserves tightening.","tokens_in":69526,"tokens_out":2398,"would_cite":true,"duration_ms":30249,"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":"The first full frequentist fit of the three-right-handed-neutrino extension maps every allowed mass and mixing from 60 MeV to 500 GeV, and finds only mild hints of new physics.","keywords":["right-handed neutrinos","seesaw mechanism","Casas-Ibarra parametrisation","profile likelihood","global fit","lepton flavour violation","CKM unitarity","Big Bang nucleosynthesis"],"falsifier":"Recalculate the profile likelihood after replacing the simplified-likelihood recasting of the DELPHI and LHC searches with a detector-level simulation for benchmark mass–mixing points; if a point excluded at 95% here becomes allowed, the central claim fails. A future NA62 or SHiP observation inside a 95% excluded region would settle it directly.","tokens_in":68394,"feed_emoji":"⚛️","tokens_out":9073,"duration_ms":88376,"temperature":0.7,"pith_summary":"Three right-handed neutrinos, the minimal extension that can give mass to all three known neutrinos, remain plausible up to surprisingly large mixings because seesaw cancellations can hide their effects. This paper performs the first full frequentist scan of that model for heavy-neutrino masses between 60 MeV and 500 GeV, combining active-neutrino oscillation data with electroweak precision observables, lepton-flavour and lepton-universality tests, CKM unitarity, neutrinoless double-$\\beta$ decay, nucleosynthesis, and every direct search that currently binds in this range. The central result is a set of profile-likelihood maps giving the strongest combined upper limits on the mixings $U^2_{\\alpha I}$ and on flavour products $U_{\\alpha I}U_{\\beta I}$, together with the allowed flavour-mixing pattern as a function of the lightest active neutrino mass. The combined data also show a modest preference, just above $2\\sigma$, for sizable tau-neutrino mixing, traceable to the $Z$ invisible width, CKM unitarity, and kaon lepton-universality measurements; the authors read these as hints rather than discovery.","feed_headline":"Three right-handed neutrinos: full map from 60 MeV to 500 GeV","feed_subtitle":"All major searches are combined into one consistent exclusion map, with mild 2-sigma hints in tau mixing.","key_machinery":"The machinery is the Casas-Ibarra parametrisation, a complex orthogonal rotation $R$ that constructs the active-sterile mixing matrix $\\Theta$ from the measured light-neutrino masses and PMNS matrix, with one-loop corrections, so every scanned point respects neutrino-oscillation data by construction. Around this, the analysis profiles a composite likelihood: direct searches enter as Poissonian or one-sided-Gaussian likelihoods calibrated to published confidence limits, indirect observables as Gaussian likelihoods, BBN as a lifetime cut, and the results are presented with a capped profile likelihood to separate exclusion from the excess regions. A differential-evolution scan over the 18-dimensional parameter space, with targeted scans saturating each experimental bound, supplies the sampled likelihood surface.","core_discovery":"The paper claims that the three-right-handed-neutrino (seesaw) parameter space below the TeV scale is now globally constrained in a statistically consistent way, and that the resulting 90% and 95% contours replace the overlay of individual exclusions. Because three heavy neutrinos allow symmetry-protected cancellations, the seesaw relation itself imposes almost no upper bound on the mixings; the bounds come from experiment: electron and muon mixings are set by fixed-target and collider searches, while tau mixing is limited mainly by electroweak precision and indirect observables. Below roughly 0.3 GeV, Big Bang nucleosynthesis demands that the total mixing $U_I^2$ be large enough for the heavy states to decay before nucleosynthesis, while oscillation data plus direct limits squeeze the flavour composition, forcing a minimum tau mixing. For the first time the flavour-mixing pattern of the three heavy neutrinos is mapped against the lightest active neutrino mass, showing that as $m_{\\nu 0}$ drops below about 0.01 meV the allowed pattern tightens and reproduces the two-heavy-neutrino limit.","pith_inferences":["Beyond the paper: the same dataset implies that if a discovery were made in the naive-seesaw 'forbidden' region, the most economical explanation would be an approximate $B-L$ symmetry rather than accidental tuning; the scan's symmetry-protected points show that region is populated.","Beyond the paper: the three excesses ($\\Gamma_{\\rm inv}$, CKM, $R^e_\\mu$) all arise from the same non-unitarity of the lepton mixing matrix, so they are not independent; a future measurement that moves one should move the inferred tau-mixing island coherently.","Beyond the paper: a testable extension would be to rerun this global fit with the updated PIENU, ATLAS, and CMS results the authors note were released after their scans, and with detector-level recasting, to check whether the contours in the $0.1$–$0.3$ GeV and $>500$ GeV regions shift."],"forward_implications":["Any future heavy-neutrino signal claimed in this mass range must lie inside the 95% allowed contours; points outside are excluded simultaneously by all data, not just by one experiment.","The current best targets for next-generation searches are the high-mass region above 80 GeV, where couplings up to $10^{-2}$–$10^{-3}$ remain allowed, and the tau-mixing window near $0.3$–$0.5$ GeV.","If the $2\\sigma$ hints persist, more precise measurements of the $Z$ invisible width, of $V_{us}$, and of $R^e_\\mu$ will sharpen a specific prediction: a heavy neutrino with $U^2_{\\tau 1}\\sim 10^{-3}$–$10^{-2}$.","The recovery of the two-heavy-neutrino flavour pattern at very small lightest-neutrino mass means that flavour-ratio measurements could distinguish $n=3$ from $n=2$ scenarios without observing all three heavy states."],"supporting_citations":[{"why":"Supplies the Casas-Ibarra parametrisation used to generate mixings that satisfy neutrino oscillation data by construction.","marker":"[44]"},{"why":"Earlier global combination of direct, indirect, and cosmological constraints that this analysis extends to n=3 with more likelihoods.","marker":"[30]"},{"why":"Reinterprets PS-191 and CHARM limits including neutral-current contributions, fixing the likelihood coefficients those searches enter with.","marker":"[38]"},{"why":"Provides the global neutrino oscillation data that form the active-neutrino likelihoods for angles, splittings, and phase.","marker":"[32]"},{"why":"Supplies the PS-191 low-mass electron and muon mixing limits used as direct-search likelihoods.","marker":"[150]"},{"why":"Supplies the CHARM beam-dump limits that dominate electron and muon mixing near and above the kaon mass.","marker":"[151]"},{"why":"Supplies the E949 kaon-decay limit on muon mixing in the 175–300 MeV window.","marker":"[154]"},{"why":"Supplies the NuTeV muon-mixing limit covering 0.25–2 GeV.","marker":"[155]"},{"why":"Supplies the DELPHI prompt and displaced-vertex bounds that dominate 0.5–80 GeV and set the key tau-mixing limits.","marker":"[156]"},{"why":"Supplies the CMS 13 TeV three-charged-lepton limits that constrain the high-mass region.","marker":"[159]"}],"fun_headline_variants":["Full frequentist map of three-neutrino seesaw","Seesaw mixings pinned by data, not symmetry","Three right-handed neutrinos: all constraints, one consistent fit","First global frequentist fit of three heavy neutrinos","Neutrino seesaw: flavour mixings from data, not symmetry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each experiment's published limit can be converted into a simple count-based likelihood calibrated to that limit, including the simplified production assumptions of collider searches, with enough accuracy for the profiling.","fun_headline_variants_meta":{"raw":{"variants":["Full frequentist map of three-neutrino seesaw","Seesaw mixings pinned by data, not symmetry","Three right-handed neutrinos: all constraints, one consistent fit","First global frequentist fit of three heavy neutrinos","Neutrino seesaw: flavour mixings from data, not symmetry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001408,"raw_usage":{"total_tokens":5730,"prompt_tokens":1026,"completion_tokens":4704,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":642,"completion_tokens_details":{"reasoning_tokens":4620}},"tokens_in":642,"tokens_out":4704,"duration_ms":35222,"temperature":1.0,"reasoning_tokens":4620,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:49:10.681834+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recalculate the profile likelihood after replacing the simplified-likelihood recasting of the DELPHI and LHC searches with a detector-level simulation for benchmark mass–mixing points; if a point excluded at 95% here becomes allowed, the central claim fails. A future NA62 or SHiP observation inside a 95% excluded region would settle it directly.","supporting_citations":[],"review_version":1}