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Threshold expansion at order alpha_s^4 for the t-tbar invariant mass distribution at hadron colliders
High Energy Physics - Phenomenology · Submitted 17 Dec 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The NNLO corrections are found to significantly enhance the cross section and reduce the perturbative uncertainties compared to the NLO calculation.
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The abstract, sentence by sentence
We calculate the leading O(alpha_s^4) contributions to the invariant mass distribution of top-quark pairs produced at the Tevatron and LHC, in the limit where the invariant mass of the t-tbar pair approaches the partonic center-of-mass energy. Our results determine at NNLO in alpha_s the coefficients of all singular plus distributions and scale-dependent logarithms in the differential partonic cross sections for q-qbar, gg -> t-tbar + X. A numerical analysis showing the effects of the NNLO corrections on the central values and scale dependence of the invariant mass distribution is performed. The NNLO corrections are found to significantly enhance the cross section and reduce the perturbative uncertainties compared to the NLO calculation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the leading O(alpha_s^4) contributions to the invariant mass distribution of top-quark pairs produced at the Tevatron and LHC, in the limit where the invariant mass of the t-tbar pair approaches the partonic center-of-mass energy. | contribution 1.00 | 0.97 | 0.12 | asserted 1.00 |
| s1 | Our results determine at NNLO in alpha_s the coefficients of all singular plus distributions and scale-dependent logarithms in the differential partonic cross sections for q-qbar, gg -> t-tbar + X. | result 0.81 | 0.94 | 0.19 | asserted 1.00 |
| s2 | A numerical analysis showing the effects of the NNLO corrections on the central values and scale dependence of the invariant mass distribution is performed. | contribution 0.54 | 0.95 | 0.07 | asserted 0.97 |
| s3 | The NNLO corrections are found to significantly enhance the cross section and reduce the perturbative uncertainties compared to the NLO calculation. | result 0.95 | 0.96 | 0.72 | asserted 1.00 |
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The paper
Original abstract
We calculate the leading O(alpha_s^4) contributions to the invariant mass distribution of top-quark pairs produced at the Tevatron and LHC, in the limit where the invariant mass of the t-tbar pair approaches the partonic center-of-mass energy. Our results determine at NNLO in alpha_s the coefficients of all singular plus distributions and scale-dependent logarithms in the differential partonic cross sections for q-qbar, gg -> t-tbar + X. A numerical analysis showing the effects of the NNLO corrections on the central values and scale dependence of the invariant mass distribution is performed. The NNLO corrections are found to significantly enhance the cross section and reduce the perturbative uncertainties compared to the NLO calculation.
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References
How the literature uses it
28 arXiv papers cite this in 55 sentences
Papers citing it · 32 sentences without a confident label
Builds on it 1 paper
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Since a detailed analysis of soft-gluon resummation for the pair-invariant mass distribution was carried out with the counting $m_t∼M$ in [ref] , our main motivation is to study to what extent these results can be improved through the additional layer of resummation in the small-mass limit $m_t≪M$.
Soft-gluon resummation for boosted top-quark production at hadron colliders · Numerical studies · 0.89
Uses its method or tool 4 papers
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Following the procedure employed in [ref] and in the papers devoted to the calculation of differential distributions for top-quark pair production [ref] , we consider two different kinematic schemes, each of which has its own threshold limit.
NNLL Momentum-Space Resummation for Stop-Pair Production at the LHC · Notation · 0.96
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It was shown in [ref] that the leading singular terms in the hard-scattering kernels can be generated by replacing the Laplace variable $L$ with a derivative $∂_η$ with respect to an auxiliary variable $η$, which is later set to 0.
Approximate NNLO Predictions for the Stop-Pair Production Cross Section at the LHC · Preliminaries · 0.83
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The definition of and procedure for calculating the hard functions in the quark annihilation and gluon fusion channels is in exact analogy with [ref] .
Associated production of a top pair and a Higgs boson beyond NLO · Soft-gluon resummation for $tt̅H$ hadroproduction · 0.88
Uses its data or values 1 paper
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The coefficients proportional to powers of $L ≡ln( M^2 / (𝒩̅^2 μ^2))$ are determined by NNLL soft-gluon resummation and were obtained in [ref] .
Top-quark pair production at high invariant mass: an NNLO soft plus virtual approximation · Notation · 0.82
Compares with it 1 paper
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Notice that within errors our SM prediction for $$ is in good agreement with recent theoretical calculations, that include effects of logarithmically enhanced NNLO terms [ref] .
Top-Quark Forward-Backward Asymmetry in Randall-Sundrum Models Beyond the Leading Order · Numerical Analysis · 0.97
Cites it as support 1 paper
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In fact, numerical comparisons of exact NLO results with the leading terms in the soft limit show good agreement only if the delta-function terms are included to achieve a full virtual plus soft approximation [ref] .
The NNLO soft function for the pair invariant mass distribution of boosted top quarks · Introduction · 0.97
Cites it as background 13 papers
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For what concerns the distributions differential with respect to the top-quark pair invariant mass and scattering angle, a NNLL resummation scheme was presented in [ref] , while approximate NNLO formulas were first published in [ref] .
Top-Quark Pair Production Beyond Next-to-Leading Order · INTRODUCTION · 0.85
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Recently, these have been supplemented with soft-gluon resummation at next-to-next-to-leading logarithmic (NNLL) accuracy in [ref] , building on the next-to-leading logarithmic (NLL) results of [ref] .
Soft-gluon resummation for boosted top-quark production at hadron colliders · Introduction · 0.87
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We also review the derivation of the approximate NNLO formula, which has been presented first in [ref] .
Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders · Introduction · 0.86
What it cites · 44 sentences without a confident label
Uses the method or tool of 2 papers
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It is convenient to avoid this complication by working instead with the Laplace transform of the soft function [ref] , defined as [equation] Whereas the soft function contains distributions, the Laplace-transformed function is a polynomial in its first argument and satisfies a local evolution equation.
Threshold Resummation in Momentum Space from Effective Field Theory · NNLO corrections at threshold · 0.96
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It is convenient to avoid this complication by working instead with the Laplace transform of the soft function [ref] , defined as [equation] Whereas the soft function contains distributions, the Laplace-transformed function is a polynomial in its first argument and satisfies a local evolution equation.
Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering · NNLO corrections at threshold · 0.96
Uses data or values from 1 paper
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Here and throughout the analysis we use the MSTW2008 NNLO PDFs [ref] , take $α_s(M_Z)=0.117$ with three-loop running in the $MS$ scheme with five active flavors, and use $m_t=173.1$ GeV in the pole scheme.
Uncertainties on alpha_S in global PDF analyses and implications for predicted hadronic cross sections · Phenomenological applications · 0.93
Compares with 1 paper
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Our results for $D_1$, $D_2$, $D_3$, and the $μ$-dependent terms agree with [ref] , while the exact result for $D_0$ contains process-dependent two-loop effects and is new.
Next-to-next-to-leading order soft-gluon corrections in top quark hadroproduction · NNLO corrections at threshold · 0.99
Cites as background 11 papers
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Current theoretical predictions are based on next-to-leading order (NLO) calculations of the total cross section [ref] and differential distributions [ref] in fixed-order perturbation theory, supplemented with soft gluon resummation to next-to-leading-logarithmic (NLL) order [ref] .
On the Soft-Gluon Resummation in Top Quark Pair Production at Hadron Colliders · Introduction · 0.93
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Current theoretical predictions are based on next-to-leading order (NLO) calculations of the total cross section [ref] and differential distributions [ref] in fixed-order perturbation theory, supplemented with soft gluon resummation to next-to-leading-logarithmic (NLL) order [ref] .
Sudakov Resummation and Finite Order Expansions of Heavy Quark Hadroproduction Cross Sections · Introduction · 0.93
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Current theoretical predictions are based on next-to-leading order (NLO) calculations of the total cross section [ref] and differential distributions [ref] in fixed-order perturbation theory, supplemented with soft gluon resummation to next-to-leading-logarithmic (NLL) order [ref] .
Next-to-next-to-leading order soft-gluon corrections in top quark hadroproduction · Introduction · 0.93
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