Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD

Abstract

We study the splitting functions for the evolution of fragmentation distributions and the coefficient functions for single-hadron production in semi-inclusive electron-positron annihilation in massless perturbative QCD for small values of the momentum fraction and scaling variable x, where their fixed-order approximations are completely destabilized by huge double logarithms of the form alpha_s^n 1/x ln^(2n-a) x. Complete analytic all-order expressions in Mellin-N space are presented for the resummation of these terms at the next-to-next-to-leading logarithmic accuracy. The poles for the first moments, related to the evolution of hadron multiplicities, and the small-x instabilities of the next-to-leading order splitting and coefficient functions are removed by this resummation, which leads to an oscillatory small-x behaviour and functions that can be used at N=1 and down to extremely small values of x. First steps are presented towards extending these results to the higher accuracy required for an all-x combination with the state-of-the-art next-to-next-to-leading order large-x results.

21 pages, LaTeX, 4 figures (.eps). FORM file of main results included in source

References in corpus (9)

• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions
• N=4 SUSY Yang--Mills: three loops made simple(r)
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation
• Minimal Subtraction vs. Physical Factorisation Schemes in Small-x QCD
• Fully double-logarithm-resummed cross sections
• Timelike Single-logarithm-resummed Splitting Functions

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• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• Average gluon and quark jet multiplicities at higher orders
• Soft Fragmentation on the Celestial Sphere
• Leading jets and energy loss
• Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities