Quark anomalous dimensions at small x

Catani, Stefano; Hautmann, F.

doi:10.1016/0370-2693(93)90174-g

Cited by 124 publications

(241 citation statements)

References 34 publications

(36 reference statements)

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“…In particular, this is the case at the next-to-leading log x level in the MS and DIS schemes [22]. We will henceforth only consider schemes where γ − is regular at N = 0, and thus only γ + has to be resummed.…”

Section: Resumming the Singlet Anomalous Dimension Matrixmentioning

confidence: 99%

“…(2.10), and the term proportional to β 0 is the running coupling correction. Then the result is combined with the Bateman resummation: 22) where the double counting subtractions γ B, s and γ B, ss are defined from the expansion…”

Section: )mentioning

confidence: 99%

“…(3.4) gives the correct expression for the structure function, at least at the leading ln x level. This is sufficient for the determination [22] of the structure functions to the next-to-leading ln x level, and thus for the construction of the next-to-leading order of the double-leading expansion [12] of the coefficient functions, because the coefficients C i j (N, M ) have the form…”

Section: Double Leading Expansion Of the Coefficient Functionsmentioning

confidence: 99%

“…[8][9][10][11][12][13][14][15][16][17][18][19] for the "large" eigenvalue to the case n f = 0. The second ingredient is also available, at least for a small number of processes [21][22][23] for which the high-energy resummation of partonic cross sections has been performed. In particular, deep-inelastic coefficient functions have been determined in the MS and DIS (and related) schemes in ref.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, deep-inelastic coefficient functions have been determined in the MS and DIS (and related) schemes in ref. [22]. However, it is nontrivial to combine resummed coefficient functions and parton distributions at the running coupling level: the way to do this has only been recently developed in ref.…”

Section: Introductionmentioning

confidence: 99%

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Small x resummation with quarks: Deep-inelastic scattering

2008

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We extend our previous results on small-x resummation in the pure Yang-Mills theory to full QCD with n f quark flavours, with a resummed two-by-two matrix of resummed quark and gluon splitting functions. We also construct the corresponding deep-inelastic coefficient functions, and show how these can be combined with parton densities to give fully resummed deep-inelastic structure functions F 2 and F L at the next-to-leading logarithmic level. We discuss how this resummation can be performed in different factorization schemes, including the commonly used MS scheme. We study the importance of the resummation effects by comparison with fixed-order perturbative results, and we discuss the corresponding renormalization and factorization scale variation uncertainties. We find that for x below 10 −2 the resummation effects are comparable in size to the fixed order NNLO corrections, but differ in shape. We finally discuss the phenomenological impact of the small-x resummation, specifically in the extraction of parton distribution from present day experiments and their extrapolation to the kinematics relevant for future colliders such as the LHC.

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Section: Resumming the Singlet Anomalous Dimension Matrixmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Double Leading Expansion Of the Coefficient Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Small x resummation with quarks: Deep-inelastic scattering

2008

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Isolated prompt photon pair production at hadron colliders with k T -factorization

Lipatov

2013

J. High Energ. Phys.

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In the framework of the k T -factorization approach, the isolated prompt photon pair production in pp and pp collisions at high energies is studied. The consideration is based on the quark-antiquark annihilation, quark-gluon scattering and gluon-gluon fusion subprocesses, where the non-zero transverse momenta of incoming partons are taken into account. The unintegrated quark and gluon densities in a proton are determined using the Kimber-MartinRyskin prescription. The numerical analysis covers the total and differential production cross sections and extends to specific angular correlations between the produced prompt photons. Theoretical uncertainties of our evaluations are studied and comparison with the NLO pQCD calculations is performed. The numerical predictions are compared with the recent experimental data taken by the D∅, CDF, CMS and ATLAS collaborations at the Tevatron and LHC energies.

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Four-loop splitting functions at small x

Bonvini

Marzani

2018

J. High Energ. Phys.

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Abstract:We consider the expansion of small-x resummed DGLAP splitting functions at next-to-leading logarithmic (NLL) accuracy to four-loop order, namely next-to-nextto-next-to-leading order (N 3 LO). From this, we extract the exact LL and NLL small-x contributions to the yet unknown N 3 LO splitting functions, both in the standard MS scheme and in the Q 0 MS scheme usually considered in small-x literature. We show that the impact of unknown subleading logarithmic contributions (NNLL and beyond) at N 3 LO is significant, thus motivating future work towards their computation. Our results will be also needed in future to match NLL resummation to N 3 LO evolution. In turn, we propose an improved implementation of the small-x resummation and therefore release a new version of the resummation code (HELL 3.0) which contains these changes.

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Quark anomalous dimensions at small x

Cited by 124 publications

References 34 publications

Small x resummation with quarks: Deep-inelastic scattering

Small x resummation with quarks: Deep-inelastic scattering

Isolated prompt photon pair production at hadron colliders with k T -factorization

Four-loop splitting functions at small x

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