Next-to-next-to-leading order evolution of non-singlet fragmentation functions

Abstract

We have investigated the next-to-next-to-leading order (NNLO) corrections to inclusive hadron production in e + e − annihilation and the related parton fragmentation distributions, the ‘time-like’ counterparts of the ‘space-like ’ deep-inelastic structure functions and parton densities. We have re-derived the corresponding second-order coefficient functions in massless perturbative QCD, which so far had been calculated only by one group. Moreover we present, for the first time, the third-order splitting functions governing the NNLO evolution of flavour non-singlet fragmentation distributions. These results have been obtained by two independent methods relating time-like quantities to calculations performed in deep-inelastic scattering. We briefly illustrate the numerical size of the NNLO corrections, and make a prediction for the difference of the yet unknown timelike and space-like splitting functions at the fourth order in the strong coupling constant. In this letter we address the evolution of the parton fragmentation distributions Dh and the corresponding fragmentation functions F h a in e + e − annihilation, e + e − → γ, Z → h+X where 1 σtot d 2 σ dx dcosθ