Next-to-Leading Order Fragmentation Functions for Pions and Kaons
J. Binnewies, B. A. Kniehl, G. Kramer
TL;DR
This work delivers LO and NLO fragmentation functions for charged pions and kaons, extracted from $e^+e^-$ data near $29$ GeV and evolved via DGLAP to describe a broad energy range up to LEP1. The authors model the initial $D_a^h(x,Q_0^2)$ with a minimal six-parameter ansatz, solve the evolution in Mellin moment space, and achieve excellent fits to the TPC data while validating against multiple other datasets. They demonstrate SU(2) relations to neutral mesons and apply the FFs to inclusive charged-hadron production, confirming expected scaling violations and offering simple, practical parameterizations for use in other processes. The results provide a more up-to-date, NLO-consistent set of fragmentation functions for pions and kaons, with explicit discussion of limitations and directions for future refinement, particularly for the gluon sector.
Abstract
We present new sets of fragmentation functions for charged pions and kaons, both at leading and next-to-leading order. They are fitted to TPC data taken at energy $\sqrt s=29$~GeV and describe excellently a wealth of other $e^+e^-$ data on charged-hadron production, ranging from $\sqrt s=5.2$~GeV way up to LEP~1 energy. They also agree with data on the production of neutral pions and kaons, if one makes the natural assumption that the respective fragmentation functions are related to the charged counterparts by SU(2) symmetry. We also list simple parameterizations of the $x$ and $Q^2$ dependence of our results, which may be implemented conveniently in applications.