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.

Parametrization of nuclear parton distributions is investigated in the leading order of alpha_s. The parton distributions are provided at Q^2=1 GeV^2 with a number of parameters, which are determined by a chi^2 analysis of the data on nuclear structure functions. Quadratic or cubic functional form is assumed for the initial distributions. Although valence quark distributions in the medium x region are relatively well determined, the small x distributions depend slightly on the assumed functional form. It is difficult to determine the antiquark distributions at medium x and gluon distributions. From the analysis, we propose parton distributions at Q^2=1 GeV^2 for nuclei from deuteron to heavy ones with the mass number A~208. They are provided either analytical expressions or computer subroutines for practical usage. Our studies should be important for understanding the physics mechanism of the nuclear modification and also for applications to heavy-ion reactions. This kind of nuclear parametrization should also affect existing parametrization studies in the nucleon because "nuclear" data are partially used for obtaining the optimum distributions in the "nucleon".Comment: 16 pages, REVTeX4b5, revtex4.cls, url.sty, natbib.sty, 10pt.rtx, aps.rtx, revsymb.sty, 21 eps figures. Submitted for publication. Computer codes for the nuclear parton distributions could be obtained from http://www-hs.phys.saga-u.ac.jp Email: kumanos@cc.saga-u.ac.j

We analyze experimental data of nuclear structure-function ratios F and Drell-Yan cross section ratios for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Valence-quark distributions are determined by the F2 data at large x; however, the small-x part is not obvious from the data. On the other hand, the antiquark distributions are determined well at small x from the F2 data and at x ∼ 0.1 by the Drell-Yan data; however, the large-x behavior is not clear. Gluon distributions cannot be fixed by the present data and they have large uncertainties in the whole x region. Parametrization results are shown in comparison with the data. We provide a useful code for calculating nuclear PDFs at given x and Q 2 .