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Threshold Resummation for Dijet Cross Sections
High Energy Physics - Phenomenology · Submitted 12 Jan 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass.
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The abstract, sentence by sentence
We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factorization of coherent soft gluons from the hard scattering. The precise formulas depend on the partonic scattering angles and energies, as well as on the method used to define the jets in the final state. For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass. Other choices of dijet cross section can give, however, qualitatively different behavior, even at leading logarithm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. | contribution 1.00 | 0.95 | 0.39 | asserted 1.00 |
| s1 | This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. | contribution 0.70 | 0.63 | 0.07 | asserted 1.00 |
| s2 | The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. | interpretation 0.78 | 0.87 | 0.23 | asserted 0.99 |
| s3 | The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factorization of coherent soft gluons from the hard scattering. | interpretation 0.57 | 0.72 | 0.17 | asserted 1.00 |
| s4 | The precise formulas depend on the partonic scattering angles and energies, as well as on the method used to define the jets in the final state. | limitation 0.52 | 0.53 | 0.05 | asserted 1.00 |
| s5 | For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass. | result 1.00 | 0.95 | 0.27 | asserted 1.00 |
| s6 | Other choices of dijet cross section can give, however, qualitatively different behavior, even at leading logarithm. | result 0.89 | 0.63 | 0.10 | hedged possibility 0.77 |
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The paper
Original abstract
We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factorization of coherent soft gluons from the hard scattering. The precise formulas depend on the partonic scattering angles and energies, as well as on the method used to define the jets in the final state. For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass. Other choices of dijet cross section can give, however, qualitatively different behavior, even at leading logarithm.
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References
How later papers used it
62 later papers cite it
3 later papers by other authors are listed below: 1 built on it and 2 used its method or tool.
Builds on it 1 of 4 papers with this label
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Generalized the expression used in this paper for the dijet case to its own process.
One-loop soft anomalous dimension matrices for $t\bar t j$ hadroproduction (2022) · 1.00 · paraphrased: the licence does not allow quoting
Uses its method or tool 2 of 10 papers with this label
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Made use of the framework developed in this paper in its calculations.
Squark and gluino hadroproduction (2011) · 0.97 · paraphrased: the licence does not allow quoting
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Used an s-channel singlet-octet basis from this paper for quark-antiquark annihilation to a heavy quark pair.
Probing the Gauge Content of Heavy Resonances with Soft Radiation (2009) · 0.91 · paraphrased: the licence does not allow quoting
How the literature uses it
56 arXiv papers cite this in 134 sentences
Papers citing it · 91 sentences without a confident label
Builds on it 4 papers
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The theory of $2→4$ threshold resummation builds on the theory resummation for $2→2$ processes [ref] .
Threshold resummation for the production of four top quarks at the LHC · Methodology · 0.85
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In general, the construction of the resummation formalism for a $2 →3$ process builds up on the earlier work for the $2 →2$ processes [ref] .
On soft gluon resummation for associated single top production with a Higgs boson at the LHC · NLL resummation in the triple invariant mass kinematics: theoretical framework · 0.83
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In Mellin space we write the $ω_I$ operator as [equation] which generalizes the expression used in Ref. [ref] for the dijet case to our process.
One-loop soft anomalous dimension matrices for $t\bar t j$ hadroproduction · Definition of the soft function for $tt̅j$ hadroproduction · 1.00
Uses its method or tool 10 papers
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Our study requires us to implement NLL resummation in heavy quark production at fixed angle and rapidity [ref] .
Threshold Resummation for the Top Quark Charge Asymmetry · Introduction · 0.92
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These fixed-order predictions are next matched with the threshold resummation of soft gluon radiation to all orders and at varied accuracies [ref] , according to the standard formalism introduced in [ref] or the collinear-improved one of [ref] .
Electroweak superpartner production at 13.6 TeV with Resummino · Introduction · 0.89
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The soft function is given by [ref] [equation] with the evolution matrix written as a path-ordered exponential [equation] and $Γ_ij→(α_s(q^2))$ the soft anomalous dimension matrix.
Threshold resummation for the production of four top quarks at the LHC · Methodology · 0.81
Uses its data or values 1 paper
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The leading-order matrices $H^(0)_ab→cd$ and $S^(0)_ab→cd$ can be found in [ref] .
Toward NNLL Resummation for Hadron Production in Hadronic Collisions · Hard and Soft Matrices · 0.87
Compares with it 4 papers
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The expression given in Eq.([ref]) agrees with the one of [ref] to the required NLL accuracy.
Resummed Cross Section for Jet Production at Hadron Colliders · Resummed cross section · 0.99
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The matrix form of the factorization is the same as was found for threshold resummation for the dijet production in proton-proton collisions [ref] .
Factorization and its Breaking in Dijet Single Transverse Spin Asymmetries in $pp$ Collisions · Introduction · 0.87
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They differ from those made in Refs. [ref] by finite terms, but the collinear structure is identical.
Toward NNLL Threshold Resummation for Hadron Pair Production in Hadronic Collisions · The normalization of the soft function · 0.99
Cites it as background 20 papers
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Such resummed computations have been performed through NLO+NLL [ref] and combined [ref] with NLL threshold resummation [ref] .
Small radius inclusive jet production at the LHC through NNLO+NNLL · Introduction · 0.82
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Following the analysis of the generic soft gluon radiation in this process, see, e.g., in Refs. [ref] , one can derive the associated soft factor for the TMD factorization in matrix form of the relevant color spaces [ref] .
Factorization and its Breaking in Dijet Single Transverse Spin Asymmetries in $pp$ Collisions · Factorization Breaking Effects at NLL · 0.81
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The resummation of threshold logarithms leads to an enhancement of the cross section for large $p_T$ and has been studied in Refs. [ref] .
Threshold and jet radius joint resummation for single-inclusive jet production · Introduction · 0.81
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