Next-to-leading order evolution of polarized and unpolarized fragmentation functions

Abstract

We determine the two-loop “time-like” Altarelli-Parisi splitting functions, appearing in the next-to-leading order Q 2-evolution equations for fragmentation functions, via analytic continuation of the corresponding “space-like” splitting functions for the evolution of parton distributions. We do this for the case of unpolarized fragmentation functions and — for the first time — also for the functions describing the fragmentation of a longitudinally polarized parton into a longitudinally polarized spin- 1 2 hadron such as a Λ baryon. Our calculation is based on the method proposed and employed by Curci, Furmanski and Petronzio in the unpolarized case in which we confirm their results.