$O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space

Abstract

We calculate the Mellin moments of the $O({\alpha }_s^2)$ coefficient functions for the unpolarized and polarized fragmentation functions. They can be expressed in terms of multiple finite harmonic sums of maximal weight {\sf w = 4}. Using algebraic and structural relations between harmonic sums one finds that besides the single harmonic sums only three basic sums and their derivatives w.r.t. the summation index contribute. The Mellin moments are analytically continued to complex values of the Mellin variable. This representation significantly reduces the large complexity being present in $x$--space calculations and allow very compact and fast numerical implementations.

25 pages

Cited by in corpus (30)

• A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties
• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Global analysis of fragmentation functions to charged hadrons with high-precision data from the LHC
• Fragmentation Functions Beyond Fixed Order Accuracy
• Fully double-logarithm-resummed cross sections
• Reference results for time-like evolution up to $\mathcal{O}({\alpha }_s^3)$
• QCD threshold corrections to Higgs decay and to hadroproduction in $l^{+}{l}^{-}$ annihilation
• Automated calculation of Jet fragmentation at NLO in QCD
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Bottomoniumlike states in proton collisions: Fragmentation and resummation
• Difference Equations in Massive Higher Order Calculations
• Heavy Quark Fragmentation in $e^{+}{e}^{-}$ Collisions to NNLO+NNLL Accuracy in Perturbative QCD
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• Unwinding the rare $\Omega$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC
• An improved description of charm fragmentation data
• Global analysis of fragmentation functions to light neutral hadrons
• Pseudoscalar heavy-quarkonium hadroproduction from nonrelativistic fragmentation at NLL/NLO${}^{+}$
• Triply Heavy $\Omega$ Baryons with JETHAD: A High-Energy Viewpoint
• Tetraquark-Jet Systems at the High-Luminosity LHC
• Measurements of Normalized Differential Cross Sections of Inclusive $\eta$ Production in $e^{+}{e}^{-}$ Annihilation at Energy from 2.0000 to 3.6710 GeV
• Fragmentation Functions for ${\Xi }^{-}/{\bar{\Xi }}^{+}$ Using Neural Networks
• Structural Relations between Nested Harmonic Sums
• Multimodal Fragmentation of All-Heavy Pentaquarks: Uncertainty-Aware Predictions for Hadron Colliders
• Heavy Flavour Production in Deep--Inelastic Scattering - Two--Loop Massive Operator Matrix Elements and Beyond
• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective
• Status of Deeply Inelastic Parton Distributions
• Heavy-flavor multimodal fragmentation to $S$-wave pentacharms at next-generation hadron colliders