Determination of fragmentation functions and their uncertainties

TLDR

Uncertainty estimation is crucial for analyzing hadron‑production data at low Q² or p_T in lepton scattering and hadron‑hadron collisions. The study aims to estimate uncertainties of fragmentation functions. The authors perform a global χ² analysis of electron‑positron charged‑hadron data and use the Hessian method to determine fragmentation functions and their uncertainties, providing a user‑accessible code. The analysis shows that gluon and light‑quark fragmentation functions have large uncertainties at low Q², that KKP and Kretzer functions differ yet agree within uncertainties, and that NLO calculations improve pion and kaon FFs but not proton FFs.

Abstract

Fragmentation functions and their uncertainties are determined for pion, kaon, and proton by a global ${\ensuremath{\chi}}^{2}$ analysis of charged-hadron production data in electron-positron annihilation and by the Hessian method for error estimation. It is especially important that the uncertainties of the fragmentation functions are estimated in this analysis. The results indicate that the fragmentation functions, especially gluon and light-quark fragmentation functions, have large uncertainties at small ${Q}^{2}$. There are large differences between widely used functions by Kniehl, Kramer, and P\"otter (KKP) and Kretzer; however, they are compatible with each other and also with our functions if the uncertainties are taken into account. We find that determination of the fragmentation functions is improved in next-to-leading order (NLO) analyses for the pion and kaon in comparison with leading-order ones. Such a NLO improvement is not obvious in the proton. Since the uncertainties are large at small ${Q}^{2}$, the uncertainty estimation is very important for analyzing hadron-production data at small ${Q}^{2}$ or ${p}_{T}$ (${Q}^{2}$, ${p}_{T}^{2}\ensuremath{\ll}{M}_{Z}^{2}$) in lepton scattering and hadron-hadron collisions. A code is available for general users for calculating obtained fragmentation functions.