Reference results for time-like evolution up to $\mathcal{O}({\alpha }_s^3)$

Abstract

We present high-precision numerical results for time-like Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution in the $\overline{\mathrm{MS}}$ factorisation scheme, for the first time up to next-to-next-to-leading order accuracy in quantum chromodynamics. First, we scrutinise the analytical expressions of the splitting functions available in the literature, in both x and N space, and check their mutual consistency. Second, we implement time-like evolution in two publicly available, entirely independent and conceptually different numerical codes, in x and N space respectively: the already existing APFEL code, which has been updated with time-like evolution, and the new MELA code, which has been specifically developed to perform the study in this work. Third, by means of a model for fragmentation functions, we provide results for the evolution in different factorisation schemes, for different ratios between renormalisation and factorisation scales and at different final scales. Our results are collected in the format of benchmark tables, which could be used as a reference for global determinations of fragmentation functions in the future.

28 pages, 5 figures, 36 tables. Final version, matches published version in JHEP. Program available from http://apfel.hepforge.org/

References in corpus (25)

• Harmonic Polylogarithms
• A first unbiased global NLO determination of parton distributions and their uncertainties
• APFEL: A PDF Evolution Library with QED corrections
• A first unbiased global determination of polarized PDFs and their uncertainties
• QCDNUM: Fast QCD Evolution and Convolution
• AKK Update: Improvements from New Theoretical Input and Experimental Data
• Efficient evolution of unpolarized and polarized parton distributions with QCD-PEGASUS
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron-positron annihilation
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops
• On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions
• Identified hadron compositions in p+p and Au+Au collisions at high transverse momenta at $\sqrt{s_{{}_{NN}}}=200$ GeV
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• $O({\alpha }_s^2)$ Contributions to the longitudinal fragmentation function in $e^{+}{e}^{-}$ annihilation
• Next-to-Leading Order Evolution of Polarized and Unpolarized Fragmentation Functions
• Precision measurement of charged pion and kaon differential cross sections in electron-positron annihilation at Q = 10.52 GeV
• $O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space
• $O({\alpha }_s^2)$ Contributions to the asymmetric fragmentation function in $e^{+}{e}^{-}$ annihilation
• The hadronization of partons
• Numerical solution of $Q^2$ evolution equations for fragmentation functions
• Crossing Heavy-Flavour Thresholds in Fragmentation Functions
• Analytic Continuation of Harmonic Sums
• A New Method for Calculating Differential Distributions Directly in Mellin Space

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