{"id":"22547a53-f0a3-447f-b983-3f23a92a33d4","arxiv_id":"1210.2808","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A soft-collinear effective theory slicing method yields the top quark decay width at NNLO in QCD and the first fully differential NNLO distributions for t to W+(l+nu)b.","lead":"The authors compute how the top quark decays, including the next-to-next-to-leading order strong-force corrections, and for the first time give the full kinematic distributions of the decay products at that accuracy. The result is a precision template for measuring the top quark mass and the weak charged-current structure at the LHC.","discovery_kind":"new_method","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The τ_0 slicing residual is indirectly bounded for the inclusive width by the 10^-4 agreement with Ref. [5], but the new differential distributions have no independent cross-check and no quantified residual, so their NNLO accuracy is asserted rather than demonstrated.","rationale":"The reader correctly identifies the τ_0 slicing residual as the load-bearing premise, and correctly notes that the 10^-4 figure is the Ref. [5] comparison uncertainty, not a cutoff residual. I partially agree: for the inclusive width, the Ref. [5] agreement does provide an indirect bound on the residual (if the residual were larger than 10^-4, the agreement would be worse, assuming Ref. [5] is correct), so the reader's concern is somewhat mitigated there. The sharper gap is the differential distributions, which are the paper's headline novelty and have no independent cross-check. The paper's own sentence 'We checked that the NNLO corrections to the distributions are also stable against the cutoff τ0' asserts a check without showing it, which is exactly the kind of missing support the review should flag. The finite m_b and W width limitations are acknowledged in the body and numerically negligible (δ_bf = -0.26%, δ_Wf = -1.49% at LO, with higher-order corrections suppressed by m_b^2/m_t^2 and Γ_W/m_W), so they are not load-bearing. The public Monte Carlo is a genuine reproducibility asset. CONDITIONAL remains the right verdict; the requested quantification would move it toward ACCEPT.","tokens_in":10356,"tokens_out":13309,"duration_ms":245831,"concrete_test":"Recompute the normalized NNLO/LO1 ratio for the lepton energy and cos θ* distributions at τ_0 = 10^-4, 10^-5, 10^-6 and report the bin-by-bin variation. If the variation exceeds ~20% of the NNLO correction in any bin, the shape predictions are not yet under control; if it is well below, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's genuinely new content is the fully differential NNLO distributions (Figs. 3–6). These are computed with the same τ_0 slicing as the total width, but unlike the total width they have no independent validation: the Ref. [5] comparison is inclusive only, and the Ref. [24] comparison covers only the integrated helicity fractions extracted from cos θ*. The paper states 'We checked that the NNLO corrections to the distributions are also stable against the cutoff τ0' but reports no numbers. Because the individual Γ^(2)_i pieces reach ~2× the LO width (Fig. 1), a residual τ_0 dependence at the percent level in the shapes would be comparable to the NNLO shape correction, which is ~1/4 of the NLO correction (NLO is ~10%). The stability check is therefore load-bearing and should be quantified. This is a presentation/robustness gap, not a demonstrated error: the plateau in Fig. 1 and the Ref. [5] agreement give good reason to expect the residual is small.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript presents a next-to-next-to-leading order (NNLO) QCD calculation of the top-quark decay width and, for the first time, fully differential distributions for the semileptonic decay t → W+(l+ν)b at the same order. The method is a phase-space slicing in the variable τ = (p_b + p_X)^2/m_t^2, the invariant mass of the final-state jet: below a cutoff τ0 the distribution is obtained from the SCET factorization formula Eq. (2), using the published NNLO hard function (Ref. [13]), quark jet function (Ref. [14]) and soft function (Ref. [15]), recast in the Laplace-product form of Eq. (4); above τ0 the O(α_s^2) piece is obtained from the NLO calculation of t → W+b+jet with dipole subtraction (Refs. [16, 18]). The total width is quoted as Γ_t = Γ_t^(0)(1 + δ_bf + δ_Wf + δ_EW + δ_QCD^(1) + δ_QCD^(2)), with δ_QCD^(2) = -2.09% at m_t = 173.5 GeV (Table I), and the NNLO QCD correction agrees with Ref. [5] at the 10^-4 level. Normalized distributions in lepton energy, lepton–hardest-jet invariant mass, cos θ* and cos θ_lj are shown in Figs. 3–6, and a fit to cos θ* gives F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309.","tokens_in":10563,"tokens_out":6942,"duration_ms":134670,"significance":"If the result holds, this is a genuinely new and useful step: the first fully differential NNLO QCD prediction for top-quark decay, going beyond the self-energy-based inclusive calculations of Refs. [3–5] and providing the ingredient needed for fully differential tt̄ production and decay at NNLO. Several features deserve explicit credit. The calculation is assembled from published NNLO hard, jet and soft functions rather than from new unverified ingredients, and the inclusive number is independently cross-checked against Ref. [5] at the 10^-4 level. The scale dependence is reduced from about 1.6% at NLO to about 0.8% at NNLO (Fig. 2), which is the expected qualitative improvement and is shown rather than asserted. The extracted helicity fractions agree with the independent determination of Ref. [24]. The calculation is implemented in a public parton-level Monte Carlo (Ref. [25]), which makes the results reusable for arbitrary infrared-safe observables, and the paper is explicit that the method is closely related to q_T subtraction (Ref. [10]).","major_comments":[{"comment":"The sentence 'We checked that the NNLO corrections to the distributions are also stable against the cut-off τ0' is the only evidence offered for the slicing residual in the paper's headline new result, and no numbers or figures are given. This matters because Fig. 1 shows that the individual pieces Γ^(2)_1, Γ^(2)_2 and Γ^(2)_3 each grow to roughly twice the LO width as τ0 moves from 10^-3 to 10^-6, so the physical answer is a cancellation among large logarithms; the inclusive 10^-4 agreement with Ref. [5] validates that cancellation only for the integrated width, not for the shapes. Please quantify the check: for at least one distribution (e.g. the lepton energy spectrum of Fig. 3), show the NNLO result at two or three values of τ0 (for instance 10^-4, 10^-5, 10^-6) or quote the residual in the ratio panel, and state the τ0 value adopted for the published figures. Given that the NNLO shape correction is about one quarter of the NLO one, a residual at the percent level would be comparable to the effect being predicted.","section":"Differential distributions (paragraph preceding Figs. 3–6) and Fig. 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"No renormalization or factorization scale uncertainty is attached to any of the differential distributions, although Fig. 2 shows that scale variation is the dominant theory uncertainty for the total width and the paper motivates the distributions precisely by their use in measurements ('experimentalists can include precise corrections for the acceptance in different kinematic regions'). Please state the central scale used for Figs. 3–6 and provide a scale-variation band, or at minimum the ratio panel with μ = m_t/2 and 2m_t, for one representative distribution. Without this, the claim that the results can be used 'with the highest perturbative accuracy' is not backed by a quantified uncertainty for the observables that constitute the new content of the Letter.","section":"Differential distributions, Figs. 3–6","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The word 'complete' should be qualified: the finite bottom-mass and finite W-width corrections are included only as LO-level corrections, and the electroweak correction only at NLO, so mixed O(α_s α) and O(α_s m_b^2/m_t^2) terms are not included. Please state the accuracy bookkeeping explicitly so that 'complete' is not read as a consistent combined QCD–EW order.","section":"Abstract, first sentence","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The notation ~j(∂_η + ln(m_t^2/μ^2), μ) ~s(∂_η + ln(m_t^2/(2E_J μ)), μ) τ^η is compressed. Please state explicitly that the derivatives act on τ^η, that the product is expanded in plus distributions via Eq. (6), and that η → 0 is taken only after the expansion.","section":"Eq. (4)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The ellipsis denotes nonsingular terms in τ. Please state what class of terms is dropped and give the expected size of the residual at the τ0 actually used, so that the reader can judge whether the neglected terms are below the quoted NNLO accuracy.","section":"Eq. (2)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Please state the sign convention for δ_EW explicitly and confirm the sign against Refs. [20, 22], since the electroweak correction to the top width is quoted with the opposite sign in parts of the literature. It would also help to print the final Γ_t including all corrections, with its uncertainty, rather than only the LO width and percentage shifts.","section":"Table I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The finite-m_b and finite-Γ_W effects are included only at LO. Please give a numerical estimate of the neglected O(α_s m_b^2/m_t^2) and O(α_s Γ_W/m_W) contributions, even if only by rescaling the LO shifts by the NLO QCD correction, so that the approximation is demonstrably under control.","section":"Total width, paragraph after Table I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The fit F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309 is quoted without uncertainties, without the fit range or binning, and without noting that it is a fit to the paper's own distribution rather than an independent extraction. Please add the fit uncertainties and the procedure, and note that F_+ at 0.0017 is at the scale where the finite-m_b and NNLO corrections being advertised are relevant.","section":"Helicity fractions (paragraph discussing Fig. 5)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sum of the three NNLO pieces is evidently plotted on a separate panel or scale from the individual pieces; the caption should say so, and the text should state the τ0 value at which the final numbers of Table I are quoted.","section":"Fig. 1 and its caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The captions should record the renormalization scale and the jet-clustering parameters (e+e- kT, y_cut = 0.1), which currently appear only in the body text, so that the figures are self-contained.","section":"Figs. 3–6 captions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The explanation 'because the recoil constituents are then massive' is unclear as written; please rephrase what becomes massive and why that pushes the distributions toward the central region.","section":"Paragraph after Fig. 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The code is cited only by URL. Please give a version or tag identifier so that the numbers in this Letter can be reproduced against a fixed release.","section":"Ref. [25]","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that the agreement is 'within the range of the uncertainties of numerical calculation, which are of the order 10^-4' should specify whether 10^-4 is absolute or relative to Γ_t, and whether it refers to the authors' own numerical error or to that of Ref. [5].","section":"Comparison with Ref. [5]","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The physics is sound and the inclusive result is independently cross-checked, so I do not see a correctness problem. My reservation is that the Letter's genuinely new content, the differential distributions, rests on an unquantified slicing residual and carries no scale-uncertainty estimate, while the validation quoted (Ref. [5]) is inclusive only and the helicity-fraction comparison (Ref. [24]) is integrated. The requested additions are straightforward and do not require redoing the calculation. The 'first' novelty claim appears justified on the basis of the literature cited, and the public code is a genuine plus for the field."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"The thing to know: the inclusive NNLO width here is a recomputation, and the authors say so — it agrees with Blokland et al. at the 10^-4 level, which is a genuine independent-method confirmation. What is actually new is the fully differential t → W+(l+ν)b result at NNLO, built on the SCET factorization of the jet invariant mass distribution with published NNLO hard, jet and soft functions. That is a real step: the self-energy route cannot produce these shapes, and the paper ships a public parton-level Monte Carlo at nntopdec.hepforge.org. The construction is coherent and the ingredients are all external and published, so there is no circularity to worry about. Fig. 1 shows the expected plateau, with the three Γ(2)_i pieces each growing to roughly twice the LO width while their sum sits at 2.1% — that cancellation is the right signature, and it is convincing for the total width because Ref. [5] pins it independently. The soft spot is exactly where the stress-test note puts it. The genuinely new objects are Figs. 3–6, and they have no independent cross-check: the Ref. [5] comparison is inclusive only, and the Ref. [24] comparison covers only the integrated helicity fractions extracted from cos θ*. The paper says 'We checked that the NNLO corrections to the distributions are also stable against the cutoff τ0' and gives no numbers. Since the individual pieces reach ~2× LO, a percent-level residual in the shapes would be comparable to the NNLO shape correction itself, which is about a quarter of the NLO one. A small table of the distributions at two or three τ0 values would settle it in a line. That is a robustness-of-presentation gap, not a demonstrated error. Second, smaller: the abstract's 'complete calculation' sits awkwardly with m_b = 0 at NLO and NNLO in QCD and a W width that enters only at LO. The body is honest about this — finite m_b is added as a LO correction — so it is a framing issue, not a hidden one. The helicity fractions F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309 are a nice by-product and agree well with Ref. [24]. Who should read it: anyone doing differential top physics, top mass or helicity measurements, or assembling NNLO ttbar production plus decay. Worth a serious referee — the physics is sound and the missing piece is a number, not an argument.","headline":"The differential NNLO distributions are the real new content, and they rest on a τ0 slicing whose residual is asserted rather than quantified.","tokens_in":11237,"tokens_out":902,"would_cite":true,"duration_ms":7275,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["14.65.Ha","12.38.Bx","12.15.Lk"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The top quark's decay width and its decay-product distributions can now be computed to next-to-next-to-leading order in QCD, with electroweak, finite bottom-mass and finite W-width effects included.","keywords":["top quark decay","NNLO QCD","soft-collinear effective theory","quark jet function","phase-space slicing","W boson helicity fractions","differential decay rates","top quark mass"],"falsifier":"An independent fully differential NNLO calculation of $t$ to $W^+(l^+nu)b$ using a different subtraction scheme — antenna subtraction or a local sector method rather than slicing — that reproduces the same normalized lepton-energy, $M_{lj}$ and $cos(theta^*)$ spectra and the same $-2.09$ percent total correction would confirm the result; a persistent offset in the $cos(theta_{lj})$ or $M_{lj}$ shapes beyond the quoted theory error would show that the $tau_0$ residual was underestimated.","tokens_in":11674,"feed_emoji":"⚛️","tokens_out":2880,"duration_ms":53770,"temperature":0.7,"pith_summary":"The paper's aim is to move top-quark decay from a next-to-leading-order (NLO) prediction to a next-to-next-to-leading-order (NNLO) one, and — the part that is genuinely new — to do it *differentially*, so that the shapes of the decay products' energy, mass and angular spectra are predicted at the same accuracy as the total width. Earlier NNLO work on this process only produced the inclusive rate, and only by treating the top quark as decaying through a self-energy, which cannot yield distributions. The authors use the fact that when the final-state jet is forced to be nearly massless, the decay rate factorizes into a hard function, a jet function and a soft function, all three already known to NNLO; that gives the singular region analytically, while the remaining region is filled in with an NLO calculation of $t$ plus one jet and a tree-level $t$ plus two jets with dipole subtraction. The payoff is a total width with a residual scale dependence of about 0.8 percent instead of 1.6 percent, and normalized spectra that can be used directly as acceptance corrections in top-mass and $tWb$-coupling measurements.","feed_headline":"Top-quark decay now predicted event-by-event to NNLO","feed_subtitle":"First fully differential NNLO QCD spectra for t → W(lν)b, with W helicity fractions and a 2 percent width shift.","key_machinery":"The load-bearing device is the SCET factorization formula for the jet invariant-mass distribution in the singular limit $tau$ to 0, $frac{1}{Gamma_t^{(0)}} frac{dGamma_t}{d tau} = H(x, mu) int dk, dm^2 J(m^2, mu) S(k, mu) delta(tau - (m^2 + 2 E_J k)/m_t^2)$, written in Laplace-transformed form as a product of the hard, jet and soft functions with the $tau$-dependent plus-distribution factor that exponentiates the large logarithms of $tau_0$. This is what turns the hardest part of the double-real radiation — the region where the jet is soft or collinear — into known NNLO ingredients, leaving only a numerically tractable remainder computed with one-loop and tree-level amplitudes and dipole subtraction. The authors note the close analogy to the $q_T$ subtraction method: both exploit the universality of infrared divergences plus knowledge of the resummed singular limit.","core_discovery":"The central claim is a complete NNLO QCD calculation of the top-quark decay width together with the first fully differential NNLO QCD results for the semileptonic decay $t$ to $W^+(l^+nu)b$. Numerically, at $m_t = 173.5$ GeV the LO width is 1.5109 GeV and the corrections, in percent, are $-0.26$ from finite bottom mass, $-1.49$ from finite $W$ width, $+1.69$ from NLO electroweak, $-8.58$ from NLO QCD and $-2.09$ from NNLO QCD. The NNLO piece is obtained by splitting the jet-invariant-mass variable $tau = (p_b + p_X)^2/m_t^2$ at a cutoff $tau_0$: below the cutoff the rate follows a SCET factorization formula built from the NNLO hard, jet and soft functions, above it the rate comes from NLO $t$ to $W b$ plus one jet and tree-level $t$ to $W b$ plus two jets with dipole subtraction. The three pieces individually grow to roughly twice the LO width as $tau_0$ runs from $10^{-3}$ to $10^{-6}$, while their sum stays near 2.1 percent of the LO width — the authors present this cancellation as the validation of the method. The paper also gives normalized distributions in charged-lepton energy, lepton-hardest-jet invariant mass, $cos(theta^*)$ and $cos(theta_{lj})$, and fits the $cos(theta^*)$ distribution to obtain $W$ helicity fractions $F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309$.","pith_inferences":["The agreement between this distribution-level calculation and the older self-energy-based inclusive NNLO result is a nontrivial consistency test: the two routes share almost no technical machinery, so their matching at the $10^{-4}$ level is evidence that both are correct rather than that one reproduces the other's assumptions.","A natural extension the authors do not pursue here is polarized top decay: they note that soft radiation does not change spin and that the jet function sums over $b$ spin, which suggests the same factorization could deliver NNLO predictions for the top's spin-analysing powers, not just the $W$ helicity fractions.","If the $tau_0$ extrapolation is as benign as claimed, the same slicing strategy should transfer to charged-current $B$ decays, where the analogous singular region dominates and where the jet function would need a finite quark-mass treatment.","The quoted helicity fractions are a place where new physics in the $tWb$ vertex would show up as a shift in $F_+$; because $F_+$ is predicted at 0.0017, even a modest anomalous tensor coupling would be visible against the theory error once the experimental acceptance is corrected with these spectra."],"forward_implications":["The total top-quark width can be quoted with a residual renormalization-scale uncertainty near 0.8 percent rather than the NLO figure of about 1.6 percent, since the NNLO correction removes part of the running-coupling dependence.","Because the output is fully differential, arbitrary infrared-safe cuts can be imposed at parton level, so the same calculation can supply acceptance corrections for top-mass and $tWb$-coupling measurements rather than only a single number.","The extracted helicity fractions $F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309$, now including finite $b$ mass, finite $W$ width, NLO electroweak and NNLO QCD, agree with earlier self-energy-based determinations, which gives an independent cross-check on the $V-A$ structure of the $tWb$ vertex.","The method is presented as reusable for other heavy-to-light decays, with $B$-meson semileptonic decay named explicitly as a target.","The fully differential top decay result is the missing ingredient for a complete NNLO description of top-quark pair production followed by decay, matching the NNLO production calculations already available."],"supporting_citations":[{"why":"Supplies the NLO QCD corrections to the top decay width, the baseline this calculation improves on and cross-checks against.","marker":"[1]"},{"why":"The earlier NNLO QCD width calculation in the $m_t gg m_W$ limit, which this work extends to finite $W$ mass and to differential distributions.","marker":"[3]"},{"why":"The finite-$W$-mass NNLO width obtained from top self-energy expansions, the direct numerical comparison point for the new total width.","marker":"[5]"},{"why":"The $q_T$ subtraction method, explicitly named as the structural analogue of the slicing strategy used here.","marker":"[10]"},{"why":"Provides the NNLO hard function obtained by matching QCD onto SCET, one of the three inputs to the factorization formula.","marker":"[13]"},{"why":"Provides the massive quark jet function at NNLO, the ingredient that absorbs collinear radiation in the singular region.","marker":"[14]"},{"why":"Provides the NNLO soft function, the remaining factor in the resummed singular limit.","marker":"[15]"},{"why":"Source of the one-loop helicity amplitudes for $t$ to $W b$ plus one jet, used for the region above the $tau_0$ cutoff.","marker":"[16]"},{"why":"Supplies the dipole subtraction terms that cancel infrared divergences in the real-emission phase-space integrals.","marker":"[18]"},{"why":"The self-energy-based determination of the $W$ helicity fractions that the fitted $F_L : F_+ : F_-$ values are compared with.","marker":"[24]"}],"fun_headline_variants":["Top decay width is computed to NNLO QCD with full differential spectra","First fully differential NNLO QCD spectra are given for semileptonic top decay","W helicity fractions from NNLO top decay are 0.689, 0.0017, and 0.309","NNLO QCD shifts the top width by about 2 percent","Validation rests on cancellation between pieces, not an independent check"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The claim rests on the assumption that the neglected remainder of the $tau_0$ slicing extrapolates to zero as advertised: each of the three NNLO pieces grows to roughly twice the LO width as the cutoff shrinks, so the quoted $-2.09$ percent is a cancellation of large logarithms whose residual is asserted to be of order $tau_0$ but is not given a quantitative error band.","fun_headline_variants_meta":{"raw":{"variants":["Top decay width is computed to NNLO QCD with full differential spectra","First fully differential NNLO QCD spectra are given for semileptonic top decay","W helicity fractions from NNLO top decay are 0.689, 0.0017, and 0.309","NNLO QCD shifts the top width by about 2 percent","Validation rests on cancellation between pieces, not an independent check"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":4730,"prompt_tokens":1029,"completion_tokens":3701,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":3593}},"tokens_in":1029,"tokens_out":3701,"duration_ms":68818,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":3593,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T08:28:40.700844+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"An independent fully differential NNLO calculation of $t$ to $W^+(l^+nu)b$ using a different subtraction scheme — antenna subtraction or a local sector method rather than slicing — that reproduces the same normalized lepton-energy, $M_{lj}$ and $cos(theta^*)$ spectra and the same $-2.09$ percent total correction would confirm the result; a persistent offset in the $cos(theta_{lj})$ or $M_{lj}$ shapes beyond the quoted theory error would show that the $tau_0$ residual was underestimated.","supporting_citations":[{"cited_title":"Nucl. Phys. B 314, 1 (1989); A. Czarnecki, Phys. Lett. B 252, 467 (1990); C. S. Li, R. J. Oakes and T. C. Yuan, Phys. Rev. D 43, 3759","cited_arxiv_id":null,"evidence_quote":"Supplies the NLO QCD corrections to the top decay width, the baseline this calculation improves on and cross-checks against."},{"cited_title":"Nucl. Phys. B 544, 520","cited_arxiv_id":null,"evidence_quote":"The earlier NNLO QCD width calculation in the $m_t gg m_W$ limit, which this work extends to finite $W$ mass and to differential distributions."},{"cited_title":"Phys. Rev. Lett. 93, 062001","cited_arxiv_id":null,"evidence_quote":"The finite-$W$-mass NNLO width obtained from top self-energy expansions, the direct numerical comparison point for the new total width."},{"cited_title":"Phys. Rev. Lett. 98, 222002","cited_arxiv_id":null,"evidence_quote":"The $q_T$ subtraction method, explicitly named as the structural analogue of the slicing strategy used here."},{"cited_title":"JHEP 0811, 065 (2008); H. M. Asatrian, C. Greub and B. D. Pecjak, Phys. Rev. D 78, 114028 (2008); M. Beneke, T. Huber and X. -Q. Li, Nucl. Phys. B 811, 77 (2009); G. Bell, Nucl. Phys. B 812, 264","cited_arxiv_id":null,"evidence_quote":"Provides the NNLO hard function obtained by matching QCD onto SCET, one of the three inputs to the factorization formula."},{"cited_title":"Phys. Lett. B 637, 251","cited_arxiv_id":null,"evidence_quote":"Provides the massive quark jet function at NNLO, the ingredient that absorbs collinear radiation in the singular region."},{"cited_title":"Phys. Lett. B 633, 739","cited_arxiv_id":null,"evidence_quote":"Provides the NNLO soft function, the remaining factor in the resummed singular limit."},{"cited_title":"Nucl. Phys. B 726, 109","cited_arxiv_id":null,"evidence_quote":"Source of the one-loop helicity amplitudes for $t$ to $W b$ plus one jet, used for the region above the $tau_0$ cutoff."},{"cited_title":"Phys. Rev. D 85, 054002","cited_arxiv_id":null,"evidence_quote":"Supplies the dipole subtraction terms that cancel infrared divergences in the real-emission phase-space integrals."},{"cited_title":"Phys. Rev. D 81, 111503","cited_arxiv_id":null,"evidence_quote":"The self-energy-based determination of the $W$ helicity fractions that the fitted $F_L : F_+ : F_-$ values are compared with."}],"review_version":1}