{"id":"f6e89422-09d4-419b-9b15-9a741d05b08d","arxiv_id":"1105.5824","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Combining NNLL soft-gluon resummation in two kinematic schemes with the NLO calculation gives top-pair production cross sections at approximate NNLO, tabulated as mass-dependent fits in the pole, MS-bar, and 1S schemes with reduced perturbative uncertainty.","lead":"The authors combine soft-gluon resummation at NNLL accuracy with the fixed-order NLO calculation to produce improved predictions for the top-quark pair production cross section at the Tevatron and LHC. The result is a set of cross section fits, with uncertainties, in the pole, MS-bar, and 1S mass schemes, intended for extracting the top-quark mass from measured cross sections.","discovery_kind":"extension","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The PIM/1PI spread used in Eq. (9) to bound the dropped R(ξ) and partial C0 terms is not calibrated: both kinematics share the same threshold expansion, so their difference probes only the leading ξ-power correction, not the regular remainder that dominates away from threshold.","rationale":"The reader's weakest_assumption correctly identifies the PIM/1PI spread plus two-factor scale variation as the load-bearing premise, and correctly notes that the paper presents it as an estimate rather than a derivation. I agree with that reading and with the ACCEPT verdict. The paper's central numbers are built on published machinery ([32], [33], [35], [42]) and the new elements — the Eq. (9) combination, the MS-bar and 1S conversions in Eqs. (11), (15), (17), and the fit coefficients in Tables II and III — are internally cross-checked (two methods for the derivatives, agreement with HATHOR on the overlapping piece, fits reproducing the calculation to one permille). The scheme-conversion terms in Eq. (15) are sizable because the cross section falls steeply with m_t, so the MS-bar entries in Table IV inherit sensitivity to the derivative of the least-determined piece σ^(2); but the MS-bar and pole results land close to each other (6.64 vs 6.63 pb at the Tevatron, 157 vs 155 pb at LHC7), so this does not visibly destabilize the tables. The one place I would push beyond the reader is the calibration of the error bar: the PIM/1PI difference is not an independent estimator of R(ξ), because both kinematics share the same threshold expansion and the same hard and soft functions. That makes the quoted first error a prescription whose coverage is asserted rather than demonstrated. This is a limitation of the uncertainty estimate, not an internal inconsistency, and the authors flag R(ξ) and the partial C0 as undetermined in the text around Eq. (7). The NLO-level calibration test I propose uses only results the paper already cites, so it is a fair check rather than a request to redo the resummation. On that basis I would leave the verdict at ACCEPT; the concern bears on how much confidence to place in the width of the bands, not on whether the central values are defensible.","tokens_in":16496,"tokens_out":6168,"duration_ms":140093,"concrete_test":"Use the existing exact NLO result (Czakon–Mitov, cited as [8]) together with the threshold-approximated NLO cross section in PIM and 1PI kinematics, and define at NLO the power-correction remainder Δ_power = σ_exact,NLO − σ_threshold,NLO for LHC7 and LHC14. Compare |Δ_power| to the PIM/1PI spread evaluated at the same order. If the spread is smaller than |Δ_power| at NLO, the same proxy at approximate NNLO is not calibrated and the quoted first error in Tables I, IV, V should be inflated by at least the observed ratio; if the spread brackets |Δ_power|, the concern does not land and the error prescription is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the approximate NNLO numbers in Tables I, IV, V carry perturbative uncertainties smaller than NLO's, with the first error in each entry combining scale variation and the PIM/1PI difference per Eq. (9). The paper is candid that Eq. (7) leaves R(ξ) undetermined and C0 only partly fixed, and it uses the PIM/1PI spread as the proxy for those omissions. The concern is that this proxy is not calibrated against the quantity it is meant to bound. PIM and 1PI are two ways of organizing the same threshold expansion: same hard function, same soft anomalous dimensions, same leading-power logarithms. Their difference therefore measures the leading ξ-dependent power correction, not the regular piece R(ξ), which by construction is non-singular at ξ=0 and is precisely what dominates when the partonic threshold is far from the physical region. At LHC7 and LHC14 a large fraction of the total cross section comes from √ŝ substantially above 2m_t, so R(ξ) is not a small correction there. The only external validation offered is that the NLO and approximate NNLO ranges overlap (text around Table I), which is a consistency check on the central values, not a calibration of the error bar. If the two kinematics err in the same direction — plausible, since they share the same underlying expansion — the quoted ±8 pb at LHC7 is an underestimate, and the 'reduced below NLO' claim, while numerically true (8 < 20), would overstate the reliability of the band. This is the same soft spot the reader identified; I agree it is the load-bearing one and I am sharpening why the spread cannot be assumed to bracket R(ξ).","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript consolidates the authors' earlier effective-theory analyses of threshold resummation for top-quark pair production into a single set of predictions for the total hadronic cross section at the Tevatron, LHC7, and LHC14. The fixed-order NLO result is supplemented with NNLL soft-gluon resummation, and the resummed formulas are re-expanded to obtain approximate NNLO predictions in which the D_m coefficients of Eq. (7) are fully determined, C_0 only partly, and the regular term R(xi) is dropped. Two threshold organizations, pair invariant-mass (PIM) and single-particle-inclusive (1PI) kinematics, are computed separately and combined by the prescription of Eq. (9): the central value is their average, and the first error bar is the envelope of the two scale-varied results, so that the PIM/1PI spread enters as an estimate of power corrections to the soft limit. The paper presents numerical results at m_t = 173.1 GeV in Tables I, IV, and V for the pole, MS-bar, and 1S mass schemes, quartic fits as functions of the mass in Tables II and III, and a discussion arguing that the MS-bar scheme does not show the improved convergence reported in [3] once the full phase space rather than the s-hat -> 4m_t^2 limit is used. A Fortran implementation and a Mathematica notebook of the fit coefficients accompany the submission.","tokens_in":16809,"tokens_out":7645,"duration_ms":135759,"significance":"If the numbers hold, this is a genuinely useful Letter: it gives the experimental collaborations a documented, reproducible approximate NNLO prediction with an explicit uncertainty decomposition (scale, PIM/1PI spread, PDF, and alpha_s), together with mass-dependent fits in three schemes. The inclusion of the Fortran code and the Mathematica fit coefficients is a real strength and should be named as such; it makes the results directly usable for top-mass extraction. The paper is also candid about what approximate NNLO does and does not determine, and it cross-checks the scheme conversions both at the level of the hadronic cross section and at the level of the partonic differential cross section. The main open question is not the central values but the reliability of the quoted first error bar, which is the quantity on which the 'uncertainties reduced below NLO' claim rests.","major_comments":[{"comment":"The first error quoted in Tables I, IV, and V combines scale variation with the PIM/1PI spread, and the text is explicit that this spread is meant to estimate power corrections to the soft limit. That use is defensible: PIM and 1PI differ at subleading power in xi, so their difference does probe the leading power correction. The difficulty is that Eq. (7) also drops the regular term R(xi) and leaves C_0 only partly determined, and these are fixed-order omissions rather than soft-limit power corrections; the PIM/1PI spread does not probe them. At LHC7 and LHC14 a substantial fraction of the cross section comes from sqrt(s-hat) well above 2 m_t, where R(xi) is not small by construction. Because the headline claim is that the perturbative uncertainty is reduced below NLO, the paper should state explicitly whether the quoted first error is intended to cover R(xi) and the undetermined part of C_0, and if so on what basis. If it is not, a sentence quantifying the expected size of R(xi) (for instance from the size of the NLO regular term away from threshold) or flagging it as an additional unquantified uncertainty would make the error bar honest without changing the central values.","section":"§II–III, Eq. (9) and Tables I, IV, V","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The Letter states that its results 'represent the state-of-the-art' and 'consolidate' the earlier work, and it cites [29], [31], and [34] as prior NNLL and approximate NNLO calculations, but it gives no numerical comparison with any of them. A short comparison at m_t = 173.1 GeV for the Tevatron and LHC7, even a single line per reference, would let readers and experimentalists judge the spread among independent implementations and would substantiate the state-of-the-art claim rather than merely asserting it. This is particularly relevant because the paper's disagreement with [3] on the MS-bar scheme is explained by the s-hat -> 4m_t^2 limit, and a numerical comparison would make that explanation concrete.","section":"§V and Tables I, IV, V","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The 1S mass relation as printed is difficult to parse: the factors of alpha_s/pi and the counting 'pi alpha_s is O(1)' are not laid out in a way a reader can follow without consulting [37]. Please check the typesetting and, if possible, restate the relation in a form that makes the power counting explicit.","section":"Eq. (17)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The rows are labelled 'sigma', 'sigma + Delta sigma+', and 'sigma + Delta sigma-'. Since Delta sigma- is defined as a negative quantity in Eq. (9), the third row is the lower edge of the band; a note in the caption or a label such as 'sigma - |Delta sigma-|' would avoid the impression that the third row is an upward variation.","section":"Table II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The fit coefficients in the tables are given only for MSTW2008; the CTEQ6.6 fits are said to be in the electronic file. Please state this in the caption or the surrounding text so that a reader of the printed version knows the CTEQ fits exist.","section":"Tables II and III","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The argument that the MS-bar scheme is not optimal because the pair-production phase space is 'more indicative of the pole mass' is a physics judgment rather than a demonstrated result. It would be strengthened by quoting the numerical size of the bracketed terms in Eq. (15), or softened to a remark.","section":"§IV","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that the MS-bar scheme does not show the improved convergence found in [3] is important and is explained by the s-hat -> 4m_t^2 limit. Making the explanation quantitative, for example by quoting the size of the approximate NNLO correction in the two treatments, would help the reader judge it.","section":"§IV, comparison with [3]","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The Fortran implementation and Mathematica notebook are a strength. A sentence in the text stating what the code computes, its accuracy, and how it is invoked would help users locate and trust it.","section":"Electronic material","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a consolidation Letter that draws heavily on the authors' own prior work ([32], [33], [35], [42]) for the resummation formalism, hard and soft functions, and anomalous dimensions. That is appropriate for a Letter of this kind, and the new content (the PIM/1PI combination prescription, the three-scheme fits, and the public code) is clear enough. The editor may nonetheless wish to confirm that the novelty relative to [33] and [35] is stated explicitly, since a casual reader could take the Letter as a summary of already-published results. The main substantive point for the authors is the calibration of the first error bar, discussed in the major comments."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Short version: this is the consolidation paper from the Neubert group's SCET threshold-resummation program for top-pair production, and it is the version people will actually cite — the combined PIM/1PI prediction, the MS-bar and 1S conversions, and the polynomial fit coefficients, with code shipped alongside. The machinery itself is not new; the abstract says as much [abstract:s1], and the resummation ingredients come from the group's own [32], [33], [35], [42]. What is new is Eq. (9), the averaging of pair-invariant-mass and single-particle-inclusive kinematics with the spread folded into the error, plus the scheme conversions and the fits in Tables II and III. That is a modest but real contribution, and it is done carefully: the pole-to-MS-bar conversion is checked two ways (derivatives at the hadronic level versus the partonic level) and against HATHOR for the overlapping piece, the fits reproduce the underlying calculation to a permille, and Fortran plus a Mathematica notebook ship with the submission. The paper is also candid about what approximate NNLO leaves undetermined — the Dm coefficients are fixed, C0 only partly, R(xi) dropped — and says so at Eq. (7) rather than burying it. Credit for that; most papers in this genre do not. The soft spot is the error bar. Eq. (9) uses the PIM/1PI spread as a proxy for power corrections to the soft limit, and the paper labels it as an estimate. The stress-test's sharper version — that the spread cannot bound R(xi) — is half right. PIM and 1PI share the same threshold expansion, so their difference probes the leading xi-power correction, not the regular remainder. But because the resummed result is matched to the full NLO calculation, R is exact at NLO and only its NNLO piece is missing, so the unbound quantity is a higher-order correction rather than the whole regular term. That makes the concern real but smaller than 'the band is uncalibrated and could be badly off.' What genuinely is not validated is whether the two kinematics err in the same direction; the only check offered is NLO/approximate-NNLO overlap, which tests central values, not the width. I read that as a prescription honestly labeled, not a flaw that sinks the numbers. The disagreement with Langenfeld-Moch-Uwer on MS-bar convergence is argued from the size of the terms in Eq. (15) and the phase-space origin of the mass dependence — a physics argument, not a proof, but a checkable one, and they present it that way. Who should read it: anyone using the top-pair cross section as a mass extractor or background normalization at the Tevatron or LHC, and anyone weighing threshold-mass schemes. It deserves a serious referee; these numbers will be used.","headline":"A solid consolidation paper: the combined PIM/1PI approximate NNLO prediction with shipped code and fit coefficients, whose only real soft spot is an uncertainty band that is an honestly labeled prescription rather than a calibrated bound.","tokens_in":17566,"tokens_out":1699,"would_cite":true,"duration_ms":38703,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["14.65.Ha","12.38.Cy"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The top-quark pair production cross section is computed to approximate next-to-next-to-leading order, with a new way of estimating what the soft-gluon approximation leaves out.","keywords":["top-quark pair production","threshold resummation","soft-collinear effective theory","approximate NNLO","hadron colliders","top-quark mass schemes","parton distribution uncertainties","strong coupling uncertainty"],"falsifier":"A full NNLO calculation of the total $tbar{t}$ cross section, or a matched NLO+NNLL evaluation retaining exact soft-gluon energy dependence without the threshold expansion, whose central value falls outside the envelope quoted in Table I would show that the kinematics spread underestimates the neglected corrections.","tokens_in":17776,"feed_emoji":"⚛️","tokens_out":2983,"duration_ms":59084,"temperature":0.7,"pith_summary":"The paper asks how precisely theory can predict the total rate at which top-quark pairs are produced at the Tevatron and the LHC, given that this rate is now measured well enough to be used as a weighing scale for the top-quark mass. The authors take the standard next-to-leading-order calculation and add the tower of large logarithms that appear near threshold, resummed to next-to-next-to-leading logarithmic accuracy using soft-collinear effective theory, then re-expand the result into an approximate next-to-next-to-leading-order (NNLO) formula. Their distinctive move is to run the same resummation in two different threshold settings, pair invariant-mass kinematics and single-particle inclusive kinematics, average the two answers, and fold the spread between them into the quoted error as a stand-in for the power corrections that the soft limit discards. The payoff is a set of numbers with perturbative uncertainties smaller than at NLO: at $m_t = 173.1$ GeV with MSTW2008 NNLO PDFs they quote $155^{+8+14}_{-9-14}$ pb at the 7 TeV LHC, $855^{+52+60}_{-38-59}$ pb at 14 TeV, and $6.63^{+0.07+0.63}_{-0.41-0.48}$ pb at the Tevatron, where the first error combines scale variation with the kinematics spread. They also give the same predictions as functions of the mass in the pole, $MS$-bar, and 1S schemes, with polynomial fits and released code so that experiments can extract a mass directly from a measured cross section.","feed_headline":"Top-quark pair rate pinned down to a few percent","feed_subtitle":"Averaging two soft-gluon resummation schemes shrinks the theory error on top-pair production at the Tevatron and LHC.","key_machinery":"The load-bearing device is the threshold factorization of the partonic cross section into a hard function and a soft function, $dhat{sigma}(xi, mu_f) propto Tr[H(mu_f), S(E_s(xi)/mu_f, alpha_s(mu_f))]$, where $xi$ vanishes as extra real radiation becomes soft. Because the soft function's renormalization-group equation is non-local, it is solved by Laplace transform and inverted analytically, producing the resummed form with the factor $e^{-2gamma_E eta} Gamma(2eta) xi^{-1+2eta}$ that sums the $[ln^m xi / xi]_+$ distributions to all orders. Re-expanding this in $alpha_s(mu_f)$ gives the approximate NNLO structure with unambiguous coefficients $D_m$ of the plus-distributions, a partially determined $C_0$, and an undetermined regular piece $R(xi)$. The second device is the bookkeeping rule in Eq. (9): compute the cross section and its scale uncertainty separately in pair invariant-mass and single-particle inclusive kinematics, take the central value as the average, and take the upper and lower errors as the envelope of the two, so that the kinematics difference enters the quoted uncertainty on the same footing as scale variation.","core_discovery":"The central claim is that combining two independent threshold-resummation treatments of top-pair production, each matched to the full NLO calculation and re-expanded to approximate NNLO, yields a total cross section whose perturbative error bar is genuinely smaller than the NLO one and whose central value sits comfortably inside the NLO range. The authors verify that the two kinematics agree well once the exact dependence on the soft-gluon energy is retained in the factorization formula, which is what licenses treating their difference as an error estimate for power corrections. Applying the machinery, they find the approximate NNLO corrections to be modest in the pole scheme, so the perturbative series appears well behaved there. Converting to the $MS$-bar scheme through the three-loop pole-to-$MS$-bar relation, they report results numerically close to the pole-scheme ones, and they explicitly disagree with earlier work that found a marked improvement in convergence in the $MS$-bar scheme; they argue instead that the phase-space factors governing the Born cross section are more indicative of an on-shell mass, and that threshold masses such as the 1S mass may be the more appropriate short-distance choice at this order. The 1S-scheme numbers behave, in their words, more like the pole scheme than like the $MS$-bar scheme.","pith_inferences":["If the two kinematics err in the same direction, the quoted envelope would be too tight; a natural cross-check would be to add a third threshold variable, such as beam-thrust-like or $p_T$-based constructions, and see whether the envelope widens.","The paper's disagreement with earlier $s \\to 4m_t^2$ treatments suggests that conclusions about which mass scheme converges best are sensitive to whether exact soft-energy dependence is kept, which is a caution for any scheme-comparison argument made at the level of the threshold expansion alone.","Because the fits are given as low-order polynomials in the mass, a reader comparing an extracted mass across the pole, $MS$-bar, and 1S schemes should propagate the scheme-conversion truncation error separately from the quoted cross-section error; the paper's tables make this possible but do not tabulate it.","The released code makes the prediction reproducible, which invites a direct closure test: recompute the cross section at a mass where an independent approximate NNLO implementation exists and compare the envelopes rather than only the central values."],"forward_implications":["Experimental collaborations can convert a measured total $tbar{t}$ cross section into a top-quark mass in a well-defined renormalization scheme, using the polynomial fits in Tables II and III or the released Fortran and Mathematica code, with theory errors quoted alongside.","At the 7 TeV LHC the perturbative uncertainty on the total rate drops to roughly five percent, leaving the PDF plus $alpha_s$ uncertainty of comparable or larger size, so further progress on the prediction requires better parton distributions and a sharper $alpha_s(M_Z)$ as much as higher-order QCD.","The $alpha_s(M_Z)$ input contributes about three to four percent with MSTW2008 and one to two percent with CTEQ6.6, a contribution the authors argue should not be dropped at this level of accuracy.","Because the pole-scheme series shows no visible degradation up to approximate NNLO, the renormalon ambiguity of the pole mass is not yet a practical obstacle to mass extraction from the cross section at current precision.","The envelope method for estimating power corrections gives a template that can be reused for other threshold-dominated hadron-collider observables where two inequivalent threshold limits are available."],"supporting_citations":[{"why":"Supplies the pair invariant-mass resummation at NNLL in soft-collinear effective theory, including the hard and soft functions and the scale-setting procedure used for one half of the combination.","marker":"[33]"},{"why":"Supplies the single-particle inclusive resummation and the detailed treatment of the $C_0$ and regular-term ambiguities in the approximate NNLO formulas used here.","marker":"[35]"},{"why":"Provides the two-loop anomalous-dimension matrices for the hard and soft functions, which are what make NNLL accuracy attainable.","marker":"[42]"},{"why":"Provides the fully analytic NLO calculation that the resummed results are matched to and that sets the fixed-order baseline.","marker":"[8]"},{"why":"Supplies the MSTW2008 NNLO parton distributions and their error sets used for the central numbers and the PDF uncertainty.","marker":"[43]"},{"why":"Supplies the three-loop pole-to-$MS$-bar mass relation used to convert the cross section into the $MS$-bar scheme.","marker":"[49]"},{"why":"Defines the 1S threshold mass and gives the conversion relation used for the illustrative threshold-mass calculation.","marker":"[37]"},{"why":"Is the earlier $s to 4m_t^2$ analysis whose claim of improved convergence in the $MS$-bar scheme this paper explicitly tests and disputes.","marker":"[3]"},{"why":"Provides the independent program against which the $MS$-bar results are checked for agreement, apart from the differing NNLO piece.","marker":"[50]"}],"fun_headline_variants":["Two resummation schemes tighten the top-pair cross section","Soft-gluon resummation shrinks the top-pair theory error","Top-pair prediction holds steady across mass schemes","Scheme difference becomes the power-correction error bar","NNLL top-pair results disagree with earlier MS-bar claims"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The quoted error bar assumes that the gap between the two threshold treatments, together with a factor-of-two variation of the renormalization and factorization scales, brackets the true size of the power corrections and of the undetermined regular term that the soft limit throws away.","fun_headline_variants_meta":{"raw":{"variants":["Two resummation schemes tighten the top-pair cross section","Soft-gluon resummation shrinks the top-pair theory error","Top-pair prediction holds steady across mass schemes","Scheme difference becomes the power-correction error bar","NNLL top-pair results disagree with earlier MS-bar claims"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1415,"prompt_tokens":929,"completion_tokens":486,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":416}},"tokens_in":929,"tokens_out":486,"duration_ms":8480,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":416,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-10T17:10:16.965209+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A full NNLO calculation of the total $tbar{t}$ cross section, or a matched NLO+NNLL evaluation retaining exact soft-gluon energy dependence without the threshold expansion, whose central value falls outside the envelope quoted in Table I would show that the kinematics spread underestimates the neglected corrections.","supporting_citations":[{"cited_title":"Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders","cited_arxiv_id":"1003.5827","evidence_quote":"Supplies the pair invariant-mass resummation at NNLL in soft-collinear effective theory, including the hard and soft functions and the scale-setting procedure used for one half of the combination."},{"cited_title":"RG-improved single-particle inclusive cross sections and forward-backward asymmetry in $t\\bar t$ production at hadron colliders","cited_arxiv_id":"1103.0550","evidence_quote":"Supplies the single-particle inclusive resummation and the detailed treatment of the $C_0$ and regular-term ambiguities in the approximate NNLO formulas used here."},{"cited_title":"Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories","cited_arxiv_id":"0908.3676","evidence_quote":"Provides the two-loop anomalous-dimension matrices for the hard and soft functions, which are what make NNLL accuracy attainable."},{"cited_title":"Inclusive Heavy Flavor Hadroproduction in NLO QCD: the Exact Analytic Result","cited_arxiv_id":"0811.4119","evidence_quote":"Provides the fully analytic NLO calculation that the resummed results are matched to and that sets the fixed-order baseline."},{"cited_title":"Parton distributions for the LHC","cited_arxiv_id":"0901.0002","evidence_quote":"Supplies the MSTW2008 NNLO parton distributions and their error sets used for the central numbers and the PDF uncertainty."},{"cited_title":"Short Distance Mass of a Heavy Quark at Order \\alpha_s^3","cited_arxiv_id":"hep-ph/9907509","evidence_quote":"Supplies the three-loop pole-to-$MS$-bar mass relation used to convert the cross section into the $MS$-bar scheme."},{"cited_title":"Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution","cited_arxiv_id":"hep-ph/9904468","evidence_quote":"Defines the 1S threshold mass and gives the conversion relation used for the illustrative threshold-mass calculation."},{"cited_title":"Measuring the running top-quark mass","cited_arxiv_id":"0906.5273","evidence_quote":"Is the earlier $s to 4m_t^2$ analysis whose claim of improved convergence in the $MS$-bar scheme this paper explicitly tests and disputes."},{"cited_title":"-- HATHOR -- HAdronic Top and Heavy quarks crOss section calculatoR","cited_arxiv_id":"1007.1327","evidence_quote":"Provides the independent program against which the $MS$-bar results are checked for agreement, apart from the differing NNLO piece."}],"review_version":1}