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arXiv · 1207.5631

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

C. -H. Kom·A. Vogt·K. Yeats
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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.

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C. -H. Kom, A. Vogt, K. Yeats. 2012-07-24. Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD. https://doi.org/10.1007/jhep10(2012)033

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