{"id":"b0e490fa-8f9e-4085-92b2-fb48b8e6cc8e","arxiv_id":"1908.04643","paper_version":4,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A multidimensional template fit recovers the B0 to D*- tau+ nu_tau angular coefficients unbiasedly and model-independently despite missing neutrino information.","lead":"This paper presents a template-based fitting method that measures the twelve angular coefficients of the decay B0 to D*- tau+ nu_tau without assuming a specific new physics model, despite two missing neutrinos. The method is tested on simulated LHCb and Belle II samples and could sharpen tests of lepton flavor universality in B decays.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The q2-integrated templates are not strictly model-independent: the RIX ratio cancels only the generator's angular model, not the q2-dependence of the reconstruction smearing.","rationale":"The paper's central claim is that the twelve templates provide a model-independent measurement of the angular coefficients. For that claim to hold, the templates must be independent of the generator's q2 distribution. The weakest link is exactly the q2 integration: the ratio RIX removes the generator's angular shape, but not the conditional q2 distribution at fixed angles, which enters through q2-dependent reconstruction. The CLN-versus-ISGW2 test is too narrow to establish the claim, and the paper's own Section 3.3 acknowledges the issue by proposing q2-binned templates. This concern is load-bearing but not fatal: the method can be made model-independent by binning in q2, and the inclusive variant can be validated with additional NP-motivated q2 reweightings. The reader's verdict of CONDITIONAL is therefore unchanged. Credit is due for the realistic background treatment, toy-study validation, and clear presentation of the angular reconstruction problem.","tokens_in":41741,"tokens_out":8180,"duration_ms":92216,"concrete_test":"Using the Section 3 procedure, build hIX from the ISGW2-generated sample. Then use HAMMER to reweight the same generated events to two strongly different q2 distributions while keeping the angular basis fixed, for example a scalar/tensor NP benchmark and the CLN scheme. Rebuild M and the twelve hIX templates from each reweighted sample and compare bin-by-bin. If any hIX bin shifts by more than the template's MC statistical uncertainty, the inclusive q2-integrated method is not model-independent, and the Section 3.3 q2-binned formulation (or an explicit systematic) is required.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 constructs each hIX template by assigning a weight RIX(true angles) = DIX/M to simulated signal events, where DIX is filled with the angular function f_X and M is the angular projection of the generator's total signal model. The cancellation of the generator model is exact only if the reconstruction kernel is independent of q2 at fixed true angles. That is not the case here: Eqs. (2.1)-(2.4) estimate the tau and B momenta using the 3-pion mass, energies, and flight geometry, all of which are correlated with q2. After integrating over q2, hIX(Omega_reco) = integral d(theta) f_X(theta) integral dq2 P_gen(q2|theta) T(Omega_reco|q2,theta). The factor P_gen(q2|theta) is the generator's conditional q2 distribution at fixed true angles and is not removed by dividing by the marginal angular histogram M. Different NP models with different q2-dependent coefficients I_X(q2) therefore yield different hIX templates even though the angular functions themselves are unchanged. The CLN reweighting test in Section 3.2 does not probe this, since CLN and ISGW2 have similar q2 shapes, and Section 3.3 introduces q2-binned weights precisely because the inclusive version requires an additional assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a template-based method for measuring the q2-integrated angular coefficients IX of B0 -> D*- tau+ nu_tau decays. The twelve angular functions of Eq. (1.1) are converted into multidimensional histograms in reconstructed angular variables by weighting simulated events with the ratios RIX = DIX/M, where DIX is a histogram of the angular function f_X and M is the histogram of the generator's total angular distribution. The authors argue that this weighting cancels the generator model dependence, making the templates model independent. The method is validated on fast Monte Carlo samples against a truth-level parametric fit and with a CLN reweighting, and is extended to a realistic background mixture and a BDT classifier. Sensitivity projections are given for LHCb (9, 23, and 50 fb^-1) and Belle II (50 ab^-1) scenarios, along with a discussion of systematic uncertainties and the extrapolation to R(D*).","tokens_in":42048,"tokens_out":10811,"duration_ms":99530,"significance":"If the model-independence claim holds, this is a valuable methodological contribution to semitauonic B decays, where the missing neutrinos strongly bias the angular distribution and prevent a direct parametric fit. The paper's strengths include the explicit template construction, the validation against a truth-level fit, the use of pull distributions to demonstrate fit stability, and a realistic treatment of backgrounds and selection effects. The method is potentially applicable to other decays. However, the central claim of strict model independence is weakened by the q2-dependence of the reconstruction smearing, as detailed in the major comments; the numerical results in Sec. 5 are obtained with the inclusive version of the method, which relies on an additional assumption that is not tested with sufficient vigour.","major_comments":[{"comment":"The model-independence claim in Sec. 3 (and repeated in the abstract and conclusion) is exact only at truth level. After reconstruction, the template hIX(Omega_reco) is proportional to ∫ d(Omega_true) f_X(Omega_true) ∫ dq2 P_gen(q2|Omega_true) T(Omega_reco|q2, Omega_true), where P_gen is the generator's conditional q2 distribution at fixed true angles and T is the reconstruction kernel. Because the weights wIX = RIX(i) depend only on the true angular bin i and not on q2, a physics model with a different q2 dependence at fixed true angles, but with the same q2-integrated coefficients, yields a different template. The reconstruction given by Eqs. (2.1)-(2.4) depends on the 3-pion invariant mass and momenta, which are correlated with q2, so the kernel T is not q2-independent. The CLN reweighting test in Sec. 3.2 does not expose this residual dependence because CLN and ISGW2 have similar q2 shapes. This issue is load-bearing for the paper's central claim.","section":"Sec. 3, Eqs. (2.1)-(2.4), Sec. 3.2"},{"comment":"Section 3.3 acknowledges the additional assumption needed for the inclusive method: \"Assuming simulation accurately models all q2True->q2Reco sculpting and bin migration, the model independence of the IX measurements is preserved.\" This is in tension with the unconditional model-independence statement in Sec. 3 and the conclusion. The q2-binned extension with 12N^2 templates is the correct remedy, but it is presented as an aside and the numerical results in Sec. 5 are obtained with the inclusive method. The authors should either (a) demonstrate numerically that the inclusive templates are stable under a drastically changed q2 spectrum (for example, by reweighting the generated sample to a form factor model with a very different q2 shape and recomputing the templates and the fitted coefficients), or (b) adopt the q2-binned method for the central sensitivity projections and present the inclusive method as an approximation with a quantitative validity range.","section":"Sec. 3.3, Sec. 5"}],"minor_comments":[{"comment":"The statement that one of the eleven IX parameters is fixed by \"sum IX = 1\" is not correct; the normalisation condition in Eq. (3.2), Gamma = 1, fixes a linear combination of I1c, I1s, I2c, and I2s, not their sum. Please revise the wording.","section":"Abstract and Sec. 3.1"},{"comment":"There are formatting errors in the mathematical notation: \"12N 2 templates\" should be \"12N^2 templates\", \"y,j6s\" should be \"yj,6s\", and \"303 binning\" should be \"30^3 binning\".","section":"Eq. (3.4) and Sec. 5.4"},{"comment":"The assertion that template statistical uncertainties are negligible with one million generated events is not quantified. With 30^3 true-space bins, the average occupancy is about 37 events per bin, so the weights RIX can have substantial fluctuations in bins with small M; the resulting uncertainty on hIX is only addressed in Sec. 5.4 as an unquantified systematic. Please estimate the template uncertainty or justify the statement quantitatively.","section":"Sec. 3"},{"comment":"The uncertainty on I1s is quoted as 0.00, which is not meaningful; please give the value with an additional significant digit.","section":"Table 3 (a)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is already published in JHEP (2019), but I am reviewing the submitted version. The main technical concern is the q2-dependence of the reconstruction smearing, which is not fully addressed in the inclusive method; the q2-binned extension is the natural fix and should be promoted or its absence justified with a robustness test. The paper is otherwise well written and the demonstration is convincing within its stated assumptions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this one. First, the core trick is genuinely nice: they build twelve reconstructed-angle templates by weighting simulated events with R_IX = D_IX/M, where D_IX is the angular function histogram and M is the generator's angular model. That cancels the generator's angular shape at truth level, so the fit becomes a linear sum of twelve templates and you don't need a parametric angular model. Second, the inclusive q2-integrated version is not as model-independent as the title claims. The stress-test note is right: the cancellation only works if the reconstruction kernel is independent of q2 at fixed true angles, and it isn't. The tau momentum estimate depends on the 3-pion kinematics, which are correlated with q2; so after integrating over q2, the templates carry a memory of the generator's conditional q2 distribution. The CLN reweighting test doesn't expose this because CLN and ISGW2 have similar q2 shapes. The q2-binned version in Sec. 3.3 is the right fix, but the paper's headline demonstration is the inclusive fit.\n\nWhat the paper does well: the demonstration is otherwise solid. The binned template fit matches a truth-level parametric fit; pulls are unbiased; CLN reweighting recovers the expected coefficients. The LHCb and Belle II sensitivity studies are realistic, including backgrounds, a BDT, and feed-down. They also honestly note that the model-independent fit does worse on R(D*) than a model-dependent fit, and that systematics from MC simulation are not fully quantified.\n\nSoft spots: aside from the q2 dependence, the flight requirement is emulated with a simple cut rather than a vertex fit, and the systematic uncertainties are described but not numerically evaluated. Those are minor for a method paper. The main issue is the overstated model independence; the paper's own Sec. 3.3 suggests the authors know the inclusive version needs an extra assumption, but they don't test how much bias a strongly different q2 shape would cause.\n\nWho should read it: anyone planning semitauonic angular measurements at LHCb or Belle II, and theorists who want to connect angular observables to NP. It deserves referee time, but the referee should ask for a validation with a genuinely different q2 distribution, or for the q2-binned version to be the primary result. As is, I'd conditional-accept.","headline":"Clever template trick for semitauonic angular measurements, but the inclusive q2-integrated version is not as model-independent as claimed—the q2-binned version is the real deal.","tokens_in":42526,"tokens_out":5241,"would_cite":true,"duration_ms":53874,"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 paper shows that the twelve angular coefficients of $B^0\\to D^{*-}\\tau^+\\nu_\\tau$ can be measured from reconstructed angles alone, without assuming a form-factor model, by folding detector effects into twelve template histograms.","keywords":["angular coefficients","semitauonic B decays","template fit","model independence","missing neutrino reconstruction","R(D*)","LHCb","Belle II"],"falsifier":"Generate pseudo-data with a physics model whose angular coefficients vary strongly across $q^2$ but integrate to the Standard Model values used in the templates, apply the same reconstruction smearing, and fit with the ISGW2-built templates; any fitted coefficient that shifts by more than the toy statistical uncertainty would falsify the claimed model independence.","tokens_in":41590,"feed_emoji":"⚛️","tokens_out":7331,"duration_ms":69701,"temperature":0.7,"pith_summary":"The paper claims a way to measure all twelve angular coefficients $I_X$ of $B^0\\to D^{*-}\\tau^+\\nu_\\tau$ from reconstructed decay angles without choosing a form-factor or new-physics model. Because both the $B$ and $\\tau$ decays lose neutrinos, the reconstructed angular distribution is strongly biased, so a direct fit to the analytic angular decay rate fails. The proposed fix is to let the twelve angular functions of the decay rate become twelve template histograms in reconstructed angle space, with resolution, acceptance, and event migration included in each template; the signal fit is then a linear sum of these templates. The paper demonstrates with Monte Carlo that the fit is unbiased, works with realistic backgrounds and a multivariate classifier, and gives competitive sensitivities at the LHCb and Belle II experiments. If the method is right, angular observables of semitauonic decays can probe new physics beyond the $R(D^*)$ anomaly without form-factor systematics.","feed_headline":"Model-independent angular fit survives missing neutrinos","feed_subtitle":"A template ratio cancels the simulation model, letting 12 angular coefficients of B0→D*−τ+ντ be measured despite lost neutrinos.","key_machinery":"The load-bearing object is the reconstructed-angle template $h_{IX}$, defined for each of the twelve angular functions $X\\in\\{1c,1s,2c,2s,3,4,5,6c,6s,7,8,9\\}$. To build it, one fills a $30\\times30\\times30$ histogram $D_{IX}$ in true $(\\cos\\theta_D,\\cos\\theta_L,\\chi)$ with the angular function itself, divides by the total signal-model histogram $M$ to form the model-independent ratio $R_{IX}=D_{IX}/M$, assigns each simulated event twelve weights $w_{IX}=R_{IX}(i)$ according to its true angle bin, and fills weighted histograms in the reconstructed angles. These $h_{IX}$ may be negative in places but their sum is positive and proportional to the total decay rate; the fit PDF is the normalised sum $\\sum_X I_X h_{IX}$ with $I_{1c}$ fixed by the normalisation condition. A fourth dimension, a gradient-boosted decision-tree output built from $\\tau$ lifetime and $3\\pi$ mass variables, is added to separate signal from the dominant $B\\to D^{*-}D_s^+(X)$ backgrounds.","core_discovery":"The central claim is that model independence survives reconstruction if the templates are built from the ratio $R_{IX}=D_{IX}/M$. Here $D_{IX}$ is a finely binned histogram of the true angular function multiplying $I_X$ in Eq. (1.1), and $M$ is a histogram of the full signal model used in simulation; events are reweighted by $R_{IX}$ and filled into reconstructed-angle histograms $h_{IX}$. The simulation model cancels in this ratio, so each $h_{IX}$ encodes only the detector's response to that angular component. A binned maximum-likelihood fit in $(\\cos\\theta_D,\\cos\\theta_L,\\chi)_{\\rm reco}$, with one coefficient fixed by the total-rate normalisation, then measures the remaining eleven $I_X$ without statistical bias. The paper verifies the claim by comparing the template fit to an unbinned truth-level parametric fit, by reweighting the sample to the CLN form-factor scheme and recovering the same coefficients, and by toy studies showing pull distributions centred at zero with unit width.","pith_inferences":["The paper tests model independence with only two form-factor schemes; a sharper check would be to reweight the true $q^2$ distribution to extreme shapes and verify that the reconstructed templates do not move, which is a direct consequence of the claimed ratio cancellation that the authors do not report.","If the templates are truly model-independent, the same method can be used as a null test in $B\\to D^{(*)}l\\nu$ decays, where better angular resolution should make agreement with Standard Model predictions much stricter; the paper suggests this but does not quantify it.","A practical extension would split the sample by $\\tau$ charge to measure $I_X$ and $\\bar I_X$ separately as a CP test; the paper notes this possibility but gives no sensitivity estimate.","The systematic uncertainty from limited Monte Carlo template statistics is mentioned but not evaluated; a natural extension is to propagate template bin fluctuations in the toy studies and show that the fitted coefficients remain unbiased."],"forward_implications":["At 9 fb$^{-1}$ of LHCb data the fit is already unbiased: the signal fraction is recovered to $f_{\\rm sig}=0.116\\pm0.010$ and the derived $D^*$ longitudinal polarisation is $F_L(D^*)=0.368\\pm0.047$, statistical only.","At 50 fb$^{-1}$ the eleven free coefficients are measured with absolute statistical uncertainties between 0.01 and 0.06, and $F_L(D^*)=0.446\\pm0.010$.","A Belle II sample of roughly 7000 three-prong tagged events gives coefficient uncertainties competitive with 23 fb$^{-1}$ of LHCb data, because tagging the other $B$ improves the $B^0$ momentum constraint and the sample is cleaner.","The same template construction extends to $N$ bins in true $q^2$: it needs $12N^2$ templates but still only $11N$ angular coefficients plus $N$ signal fractions, so model independence is preserved when $q^2$ migration is modelled.","The measured signal fraction can be converted to $R(D^*)$, but with worse statistical precision than a model-dependent fit (8.6% versus below 3% at 9 fb$^{-1}$); the angular coefficients themselves are the model-independent new-physics probes."],"supporting_citations":[{"why":"Supplies the full angular decay-rate expression, the normalisation condition, and the Standard Model $I_X$ values used as validation targets.","marker":"[30]"},{"why":"Provides the LHCb signal yield, background fractions, and $\\tau$ flight requirement that define the realistic data model.","marker":"[8]"},{"why":"Fast heavy-quark decay simulation used to generate all signal and background samples with LHCb-like resolution and acceptance.","marker":"[33]"},{"why":"The ISGW2 form-factor model generates the nominal signal sample from which templates are built.","marker":"[37]"},{"why":"The CLN form-factor scheme supplies the alternative model used in the reweighting validation that the templates must reproduce.","marker":"[43]"},{"why":"Reweighting tool used to apply the CLN scheme to the generated sample in the validation test.","marker":"[44]"},{"why":"Defines the decay-angle basis and motivates angular analysis as a model-independent tool from $B^0\\to K^{*0}\\mu^+\\mu^-$.","marker":"[32]"}],"fun_headline_variants":["Template ratio cancels simulation model in angular fit","Unbiased angular coefficients with missing neutrinos","Model independence survives lost neutrinos in B→D*τν","Reweighting erases model bias for B→D*τν angular coefficients","No model bias: angular coefficients from B→D*τν with lost neutrinos"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the simulated detector response packed into each template is the same for every possible underlying physics model; if data and simulation disagree in a way the templates cannot absorb, the measured $I_X$ values are biased.","fun_headline_variants_meta":{"raw":{"variants":["Template ratio cancels simulation model in angular fit","Unbiased angular coefficients with missing neutrinos","Model independence survives lost neutrinos in B→D*τν","Reweighting erases model bias for B→D*τν angular coefficients","No model bias: angular coefficients from B→D*τν with lost neutrinos"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000862,"raw_usage":{"total_tokens":3722,"prompt_tokens":910,"completion_tokens":2812,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":2723}},"tokens_in":526,"tokens_out":2812,"duration_ms":20117,"temperature":1.0,"reasoning_tokens":2723,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:36:35.321145+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate pseudo-data with a physics model whose angular coefficients vary strongly across $q^2$ but integrate to the Standard Model values used in the templates, apply the same reconstruction smearing, and fit with the ISGW2-built templates; any fitted coefficient that shifts by more than the toy statistical uncertainty would falsify the claimed model independence.","supporting_citations":[{"cited_title":"Isgur, D","cited_arxiv_id":null,"evidence_quote":"The ISGW2 form-factor model generates the nominal signal sample from which templates are built."},{"cited_title":"Duell, F","cited_arxiv_id":null,"evidence_quote":"Reweighting tool used to apply the CLN scheme to the generated sample in the validation test."}],"review_version":1}