Determination of fragmentation functions and their uncertainties from e⁺ + e⁻ → h + X data

Fragmentation functions are determined for pions, kaons, and nucleons by a global analysis of charged‐hadron production data in electron‐positron annihilation. The optimum functions are obtained in both leading order (LO) and next‐to‐leading order (NLO) of α_s. It is important that uncertainties of the fragmentation functions are estimated in this work by the Hessian method. We found that the uncertainties are large at small Q² and that they are generally reduced in the NLO in comparison with the LO ones. We supply a code for calculating the fragmentation functions and their uncertainties for the pions, kaons, and nucleons at given z and Q².