Top-Quark Decay at Next-to-Next-to-Leading Order in QCD

Chong Sheng Li; Hua Xing Zhu; Jun Gao

REVIEW

Top-Quark Decay at Next-to-Next-to-Leading Order in QCD

Jun Gao, Chong Sheng Li, Hua Xing Zhu

High Energy Physics - Phenomenology · Submitted 10 Oct 2012 · 25 references

Pith's verdict: The differential NNLO distributions are the real new content, and they rest on a τ0 slicing whose residual is asserted rather than quantified.

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arXiv ID1210.2808 (version 3)

Pith IDWJCC7ISR, Pith's permanent record of this paper and its review

CitationChong Sheng Li, Hua Xing Zhu, Jun Gao. "Top-Quark Decay at Next-to-Next-to-Leading Order in QCD." arXiv:1210.2808 (2012). https://pith.science/paper/WJCC7ISR

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Editor's note

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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.

Referee report

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 objections (2)

[Differential distributions (paragraph preceding Figs. 3–6) and Fig. 1] 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.
[Differential distributions, Figs. 3–6] 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.

Minor objections (11)

[Abstract, first sentence] 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.
[Eq. (4)] 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.
[Eq. (2)] 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.
[Table I] 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.
[Total width, paragraph after Table I] 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.
[Helicity fractions (paragraph discussing Fig. 5)] 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.
[Fig. 1 and its caption] 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.
[Figs. 3–6 captions] 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.
[Paragraph after Fig. 4] 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.
[Ref. [25]] 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.
[Comparison with Ref. [5]] 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].

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The paper

The paper claims

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.

The reading

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.

What carries the argument

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.

Extended reading notes

Core claim

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 $F_L : F_+ : F_- = 0.689 : 0.0017 : 0.309$.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

Original abstract

We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and $W$ boson width effects. In particular, we also show the first results of the fully differential decay rates for top-quark semileptonic decay $t\to W^+(l^+\nu)b$ at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,681 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.69 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.09 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and $W$ boson width effects. In particular, we also show the first results of the fully differential decay rates for top-quark semileptonic decay $t\to W^+(l^+\nu)b$ at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and $W$ boson width effects.	contribution 0.95	0.96	0.78	asserted 1.00
s1	In particular, we also show the first results of the fully differential decay rates for top-quark semileptonic decay $t\to W^+(l^+\nu)b$ at next-to-next-to-leading order in QCD.	result 0.61	0.96	0.20	asserted 1.00
s2	Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory.	method 1.00	0.57	0.04	asserted 1.00
s3	Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.	interpretation 0.88	0.63	0.20	asserted 0.66

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.78.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. Separate contributions of the NNLO QCD corrections

**Figure 2.** FIG. 2. Renormalization scale dependence of the NLO and

**Figure 3.** FIG. 3. Energy distribution of the charged lepton from top

**Figure 5.** FIG. 5. Angular distribution of the charged lepton from top

**Figure 6.** FIG. 6. Angular distribution of the charged lepton from top

Showing 5 of the paper's 6 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1210.2808 by the authors.

References

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A new matching scheme, UN2LOPS, yields the first fully exclusive Drell-Yan event generator that is simultaneously NNLO-accurate in QCD and showered, and it agrees with independent fixed-order codes at the permille level.
Infrared Structure at NNLO Using Antenna Subtraction
hep-ph 2013-01 accept novelty 6.0 of 10

The infrared pole structure of NNLO QCD corrections can be written as a sum of integrated dipoles built from antenna functions and mass factorisation kernels, reproducing Catani's one- and two-loop factorisation formulae.
SMEFTsim 3.0 -- a practical guide
hep-ph 2020-12 accept novelty 5.0 of 10

SMEFTsim 3.0 ships ten validated UFO models covering the complete Warsaw basis at tree level, adding two top-sector flavor scenarios, dimension-7 Higgs-gluon matching, and linearized propagator corrections for the W, ...
The gluon-fusion production of Higgs boson pair: N$^3$LO QCD corrections and top-quark mass effects
hep-ph 2019-12 accept novelty 5.0 of 10

Third-order (N3LO) QCD corrections to gluon-fusion Higgs pair production, combined with top-quark mass effects via three approximation schemes, cut scale uncertainties fourfold relative to NNLO.
Measurements of top-quark pair differential and double-differential cross-sections in the $\ell$+jets channel with $pp$ collisions at $\sqrt{s}=13$ TeV using the ATLAS detector
hep-ex 2019-08 accept novelty 5.0 of 10

ATLAS presents single- and double-differential top-quark pair cross-sections in the l+jets channel at 13 TeV, finding good overall agreement with predictions but tensions in boosted high-pT tails.
Power Corrections in the N-jettiness Subtraction Scheme
hep-ph 2016-12 accept novelty 5.0 of 10

The authors derive the leading-logarithmic power corrections to N-jettiness subtraction through next-to-next-to-leading order for color-singlet production and show they let the subtraction cutoff be relaxed roughly tenfold.
Color singlet production at NNLO in MCFM
hep-ph 2016-05 conditional novelty 5.0 of 10

MCFM v8.0 ships validated NNLO QCD predictions for pp to H, Z, W, ZH, WH and diphoton, with quantified jettiness-cut systematics and cluster scaling benchmarks.
Higgs boson decay into b-quarks at NNLO accuracy
hep-ph 2015-01 accept novelty 5.0 of 10

The paper validates a general NNLO subtraction scheme by applying it to Higgs decay into b-quarks, showing analytically that its integrated counterterms cancel the infrared poles of the two-loop amplitude and reproduc...
Higgs-boson production through gluon fusion at NNLO QCD with parton showers
hep-ph 2014-07 conditional novelty 5.0 of 10

UN2LOPS matching is extended to gluon-fusion Higgs production, with two refinements to the matching formula and a new fully differential NNLO event generator in Sherpa that agrees with HNNLO at the permille level.
Les Houches 2013: Physics at TeV Colliders: New Physics Working Group Report
hep-ph 2014-05 conditional novelty 5.0 of 10

Twenty contributed studies from the 2013 Les Houches New Physics working group cover Higgs coupling fits, vector-like quark and composite Higgs benchmarks, SUSY constraints, flavour observables and dark matter, includ...
$O(\alpha_s^2)$ corrections to fully-differential top quark decays
hep-ph 2013-01 conditional novelty 5.0 of 10

A sector-decomposition plus FKS calculation yields fully differential NNLO QCD corrections to semileptonic top decay, reproducing known total-rate and helicity-fraction results and adding new kinematic distributions.
Top and Beauty synergies in SMEFT-fits at present and future colliders
hep-ph 2020-12 conditional novelty 4.0 of 10

Combining top-quark, Z to b bbar, and b to s observables in a global SMEFT fit breaks flat directions, and adding a future lepton collider would constrain all eleven considered Wilson coefficients, including four-ferm...
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report
hep-ph 2018-03 accept novelty 4.0 of 10

The report documents the state of precision Standard Model calculations for the LHC in 2017, including new NNLO subtraction and grid techniques, a tuned comparison of electroweak one-loop tools, and a prioritized list...
Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector
hep-ph 2016-10 accept novelty 3.0 of 10

The report fixes the community's baseline numbers for Higgs boson production and decay at the 13 TeV LHC, including a 48.6 pb gluon-fusion cross section at N3LO with an explicit uncertainty budget.
Prospects for charged Higgs searches at the LHC
hep-ph 2016-07 accept novelty 3.0 of 10

A survey of charged-Higgs phenomenology in non-supersymmetric multi-doublet models concludes that Model II is pushed above roughly 480 GeV by B to Xs gamma, while Models I and X and dark-sector variants still allow a ...
High precision fundamental constants at the TeV scale
hep-ph 2014-05 conditional novelty 3.0 of 10

The report compiles 2014 determinations of the strong coupling and the top quark mass, shows that independent extractions scatter beyond their quoted uncertainties, and recommends a standing working group plus scheme-...
The Semileptonic B Frontier: LHC, B-factories, Lattice QCD & the Hunt for Precision
hep-ph 2026-10 accept novelty 2.0 of 10

A comprehensive review of semileptonic B decays, including charged-current and neutral-current processes, with emphasis on CKM determinations, LFU tests, and the interplay between experiment and theory.
Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
hep-ph 2025-04 unverdicted novelty 2.0 of 10

The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
Snowmass 2013 Top quark working group report
hep-ph 2013-11 accept novelty 2.0 of 10

The report compiles community projections showing that a future lepton collider can measure the top mass to about 100 MeV and top couplings an order of magnitude better than the high-luminosity LHC.

How later papers used it

105 later papers cite it

Evidence: substantial. 89 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 24 of the 132 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

7 later papers by other authors are listed below: 5 used its data or values, 1 compared its own results with it and 1 cited it as support. 2 more papers by the same authors are listed: 2 used its method or tool.

Uses its method or tool 2 of 10 papers with this label · 2 by the same authors

By the same authors

Based its calculation of the NNLO decay width of the charged Higgs boson or top quark on this paper's phase space slicing method.

Decay of the charged Higgs boson and the top quark in two-Higgs-doublet model at NNLO in QCD (2022) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
Employed phase-space slicing at NNLO from this paper, a generalization of the qT-subtraction concept of Catani and Grazzini.

Charm-quark production in deep-inelastic neutrino scattering at NNLO in QCD (2016) (same authors) · 0.97 · paraphrased: the licence does not allow quoting

Uses its data or values 5 of 14 papers with this label

The resulting branching ratios are given by [equation] with $Γ_t ≡Γ(t→bW) = 1.32$ GeV being the total width calculated at Next-to-next-to-LO in QCD [ref] and $Γ(t→qX)$ is the corresponding top FCNC partial width [ref] .

Top quark flavor changing neutral currents at Future Linear Colliders (2024) · Top quark FCNC decays triggered by dark matter · 1.00
This can in turn be interpreted in terms of a limit on the branching fraction thanks to the relation [equation] with $Γ_=1.32$ at NNLO [ref] and $Γ_^=1 = Γ_^=1 = 0.19$.

Search for flavor-changing neutral current interactions of the top quark and the Higgs boson decaying to a bottom quark-antiquark pair at $\sqrt{s}$ = 13 TeV (2021) · Results · 1.00
These upper limits on the branching fractions can be translated into upper limits on the coupling strengths using the relations: [equation] where the total top quark width is $Γ_ = 1.32$ [ref] , and the partial width for the FCNC decay process of the top quark is $Γ_ = Γ_ = 0.184$for $κ_ = κ_ = 1$.

Search for the flavor-changing neutral current interactions of the top quark and the Higgs boson which decays into a pair of b quarks at $\sqrt{s}=$ 13 TeV (2017) · Results · 0.99
We calculate $Γ_t = Γ_SM + ∑_jΓ(t →H_1,2^+d_j)$, where the NLO (EW) + NNLO (QCD) Standard Model result $Γ_SM = 1.322$ GeV is taken from [ref] , while $∑_jΓ(t →H_1,2^+d_j)$ is computed from Eq. [ref] summed over all the relevant channels.

Constraining CP4 3HDM with top quark decays (2021) · Top quark width · 1.00
The top-quark mass ($m_t$) and width were set to 172.5 and 1.32 [ref] , respectively, in all MC event generators.

Measurements of top-quark pair differential and double-differential cross-sections in the $\ell$+jets channel with $pp$ collisions at $\sqrt{s}=13$ TeV using the ATLAS detector (2019) · Signal simulation samples · 0.99

Compares with it 1 of 5 papers with this label

Checked that its assembled fully differential spin-averaged top quark decay width agrees within numerical uncertainties with this paper's program NNTopDec.

Higher order corrections to spin correlations in top quark pair production at the LHC (2019) · 0.98 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 2 papers with this label

Treated the decay part at tree level only, citing this paper as evidence that radiative corrections at the level of the decay are very small in the Standard Model.

Probing anomalous $Wtb$ couplings at the LHC in single top quark production through $t$-channel (2018) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

104 arXiv papers cite this in 131 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 67 sentences without a confident label

Uses its method or tool 10 papers

In this work we employ the $N$-jettiness subtraction scheme [ref] to perform the evaluation of the NNLO cross section.

NNLO predictions for Z-boson pair production at the LHC · Details of the calculation · 1.00
Our calculation of the NNLO decay width of charged Higgs boson or top quark is based on the phase space slicing method [ref] .

Decay of the charged Higgs boson and the top quark in two-Higgs-doublet model at NNLO in QCD · Phase space slicing method · 0.99
We can thus replace the zero-jet by a full $q_T$-vetoed NNLO calculation, using the cutoff method [ref] , and complete the cross section using the one-jet [ref] : Each event removed from the one-jet bin by means of the emission probability $1-Π_0(t,μ_Q^2)$ is added to the zero-jet bin.

Higgs-boson production through gluon fusion at NNLO QCD with parton showers · UN$^2$LOPS matching · 0.96

Uses its data or values 14 papers

The resulting branching ratios are given by [equation] where $Γ_t ≡Γ(t→b W) = 1.32 GeV$ calculated at Next-to-Next-to-Leading Order in QCD including the finite mass and width effects and Next-to-Leading Order electroweak corrections [ref] .

Dark matter as the trigger of flavor changing neutral current decays of the top quark · Top quark FCNC decays · 1.00
The resulting branching ratios are given by [equation] with $Γ_t ≡Γ(t→bW) = 1.32$ GeV being the total width calculated at Next-to-next-to-LO in QCD [ref] and $Γ(t→qX)$ is the corresponding top FCNC partial width [ref] .

Top quark flavor changing neutral currents at Future Linear Colliders · Top quark FCNC decays triggered by dark matter · 1.00
For a top-quark mass of 172.5 GeV the predicted width is 1.322 GeV, including NNLO QCD, finite $b$-quark and $W$ masses, and NLO electroweak corrections [ref] .

Extracting the Top-Quark Width from Non-Resonant Production · Existing Calculations and Measurements · 0.92

Compares with it 5 papers

The above results of $δ_b^(0),δ_W^(0),δ_EW^(1),δ_QCD^(1)$ and $δ_QCD^(2)$ agree with the ones in [ref] when using the same input parameters.

Analytic result for the top-quark width at next-to-next-to-leading order in QCD · Introduction · 1.00
A comparison of our NLO QCD+EW prediction—with and without the additional NNLO correction of Refs. [ref] —reveals good agreement with the most recent measurement by the CMS experiment [ref] : [equation] However, the quoted experimental error is still one order of magnitude larger than the typical EW corrections of $∼ +1.3%$ addressed here.

Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay · Conclusions · 0.81
The comparison is performed with $m_t=172.5$, but the relative size of the corrections is somewhat insensitive to the precise top-quark mass [ref] .

Single-top-quark production in the $t$-channel at NNLO · Top-quark-decay corrections · 0.92

Cites it as support 2 papers

The NNLO corrections lead to a softer spectrum due to both soften of the top-quark $p_T$ and additional radiations in top-quark decay [ref] .

Top-quark mass determination from t-channel single top production at the LHC · NNLO predictions · 0.98
The full tree-level amplitude, anomalous amplitude, will be denoted $𝒫_0^ano.$, such that [equation] Since the radiative corrections at the level of the decay are very small in the SM (see e.g. [ref] ), the decay part will be considered at tree-level only.

Probing anomalous $Wtb$ couplings at the LHC in single top quark production through $t$-channel · Including anomalous $Wtb$ couplings · 0.97

Cites it as background 30 papers

The NNLO corrections were calculated in the large top quark mass limit in Refs. [ref] , and the full NNLO corrections were given in [ref] .

Decay of the charged Higgs boson and the top quark in two-Higgs-doublet model at NNLO in QCD · Introduction · 0.87
The corrections to the top-quark decay process $→$ are known at NLO [ref] and next-to-next-to-leading order (NNLO) [ref] in QCD and up to NLO for the electroweak (EW) corrections [ref] .

Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay · Introduction · 0.90
Later, the total and differential decay widths were calculated numerically [ref] , and polarized decay rates were also studied [ref] .

Analytic result for the top-quark width at next-to-next-to-leading order in QCD · Introduction · 0.96

What it cites · 4 sentences without a confident label

Compares with 1 paper

Our calculations are complementary to the NNLO QCD predictions for top-quark pair production [ref] .

Percent level precision physics at the Tevatron: first genuine NNLO QCD corrections to q qbar -> t tbar + X · Introduction · 0.93

Discussion

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