Two-Loop Anomalous Dimensions of Timelike Cut Vertices and Scaling Violation of Fragmentation Functions in QCD

Munehisa, Tomo; Okada, Hidehiko; Kudoh, Koki; Kitani, Kohei

doi:10.1143/ptp.67.609

Cited by 8 publications

(8 citation statements)

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“…However, in contrast to the case of initial state hadrons, where the evolution equations for the scaledependence of the PDFs are controlled by space-like kinematics, Q 2 ≤ 0, the scale evolution of the FFs with Q 2 ≥ 0 requires the so-called time-like splitting functions. These functions are known completely at two loops [9][10][11][51][52][53], see also refs. [54,55].…”

Section: Introductionmentioning

confidence: 94%

Four-loop non-singlet splitting functions in the planar limit and beyond

Moch¹,

Ruijl

Ueda

et al. 2017

J. High Energ. Phys.

193

188

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We present the next-to-next-to-next-to-leading order (N 3 LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N 3 LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in N = 4 super Yang-Mills theory.

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Section: Introductionmentioning

confidence: 94%

Four-loop non-singlet splitting functions in the planar limit and beyond

Moch¹,

Ruijl

Ueda

et al. 2017

J. High Energ. Phys.

193

188

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“…Then in the 1980 it has been shown by Curci, Furmanski and Petronzio [14] that the Gribov-Lipatov relation is violated. In that period several groups obtained the NLO contributions to the 'timelike' splitting functions [14,15,16,17,18,19]. In 2004 the NNLO "spacelike" splitting functions were published by Moch, Vermaseren and Vogt in Ref.…”

Section: Exiting Times For "Timelike" Qcdmentioning

confidence: 99%

Timelike structure functions and hadron multiplicities

Bolzoni¹

2013

Proceedings of XXI International Baldin Seminar on High Energy Physics Problems — PoS(Baldin ISHEPP XXI)

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In this talk we discuss the results obtained in the new approach that we recently introduced to consider and include both the perturbative and nonperturbative contributions to the evolution of the gluon and quark avarage multiplicities. We report on our progresses in solving a longstanding puzzle of QCD. The new formalism is motivated by recent important theoretical developments in timelike small-x resummation which are also discussed mostly from an historical point of view. We have extended our global analysis to fit the available data adding the strong coupling constant as a fit parameter. In this way our best fit gives α s (M z ) = 0.124 ± 0.005 and for the corresponding χ 2 we have obtained a further improvement.

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“…1 -4 at a standard reference scale, Q 2 ≃ M 2 Z , for n f = 5 effectively massless flavours. For the corresponding value α s ≃ 0.12 of the strong coupling constant, the expansions to order α 16 s are sufficient, and for some of the NNLL results required, for an accuracy of 0.1% or better down to the lowest x-values shown, x = 10 −4 . An extension of the maximal order to cover one more order of magnitude in x is definitely feasible, but does not appear to be warranted for any foreseeable analyses of experimental data.…”

Section: Resummed Timelike Splitting Functionsmentioning

confidence: 99%

“…(1.4) The leading-order (LO) and NLO contributions P (0) T and P (1) T to Eq. (1.4) have been known for a long time [12][13][14][15][16]. A direct calculation of the NNLO corrections P (2) T has not been performed so far.…”

Section: Introductionmentioning

confidence: 99%

Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation

Vogt

2011

J. High Energ. Phys.

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We have derived the coefficients of the highest three 1/x -enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e + e − annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. The resummation is found to completely remove the huge small-x spikes present in the fixed-order results, allowing for stable results down to very small values of the momentum fraction and scaling variable x. Our calculations can be extended to (at least) the corresponding α n s ln 2n−ℓ x contributions to the above quantities and their counterparts in deep-inelastic scattering.

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Two-Loop Anomalous Dimensions of Timelike Cut Vertices and Scaling Violation of Fragmentation Functions in QCD

Cited by 8 publications

References 0 publications

Four-loop non-singlet splitting functions in the planar limit and beyond

Four-loop non-singlet splitting functions in the planar limit and beyond

Timelike structure functions and hadron multiplicities

Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation

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