QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops

TL;DR

This work provides an analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in $e^+e^-$ annihilation, performing the cross-section calculation in Mellin $N$-space with unitarity cutting rules and integration-by-parts. It yields the time-like splitting and coefficient functions up to NNLO, and cross-checks the results against the established computations by Rijken and van Neerven, including higher-order $\u03b5$ terms for consistency checks. The results furnish NNLO predictions for the transverse and asymmetric fragmentation functions and NLO results for the longitudinal one, enabling refined fragmentation-function evolution and precision determinations of $
lpha_s$ from LEP and future colliders. The methodology, notably the $N$-space IBP approach and master-integral framework, opens avenues for higher-loop checks and application to other single-scale QCD observables beyond the DIS paradigm.

Abstract

We report on the analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in electron-positron annihilation. The calculation of the single-particle inclusive cross-section in time-like kinematics is performed in Mellin N-space and uses an algorithmic evaluation of inclusive phase-space integrals, based on the unitarity cutting rules and integration-by-parts. We obtain splitting functions and coefficient functions up to second order in the strong coupling alpha_s. Our results are in agreement with earlier calculations in the literature by Rijken and van Neerven.