Fragmentation functions and their uncertainties are determined for pion, kaon, and proton by a global $\chi^2$ 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 KKP (Kniehl, Kramer, and P\"otter) 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 $p_T$ ($Q^2, p_T^2 << M_Z^2$) in lepton scattering and hadron-hadron collisions. A code is available for general users for calculating obtained fragmentation functions.Comment: 16 pages, 15 figures, revtex. to be published in Phys. Rev.

Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F A 2 /F A 2 and Drell-Yan cross-section ratios σ A DY /σ A DY . The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant α s . Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at x < 0.1. However, the antiquark distributions have large uncertainties at x > 0.2. Gluon modifications cannot be fixed at this stage. Although the advantage of the NLO analysis, in comparison with the LO one, is generally the sensitivity to the gluon distributions, gluon uncertainties are almost the same in the LO and NLO. It is because current scaling-violation data are not accurate enough to determine precise nuclear gluon distributions. Modifications of the PDFs in the deuteron are also discussed by including data on the proton-deuteron ratio F D 2 /F p 2 in the analysis. A code is provided for calculating the NPDFs and their uncertainties at given x and Q 2 in the LO and NLO.

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