Index
We analyze experimental data of nuclear structure-function ratios F_2^A/F_2^{A'} 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 F_2 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 x~0.01 from the F_2 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.
Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q^2 evolution equations for parton-distribution and fragmentation functions. Because the equations cannot be solved analytically, various methods have been developed for the numerical solution. We compare brute-force, Laguerre-polynomial, and Mellin-transformation methods particularly by focusing on the numerical accuracy and computational efficiency. An efficient solution could be used, for example, in the studies of a top-down scenario for the ultrahigh-energy cosmic rays.
Nuclear parton distribution functions (NPDFs) are investigated by analyzing the data on structure functions F_2^A and Drell-Yan cross sections sigma_{DY}^{pA}. An important point of this analysis is to show uncertainties of the NPDFs by the Hessian method. The analysis indicates that the uncertainties are large for antiquark distributions at x>0.2 and gluon distributions in the whole x region. We also discuss a nuclear effect on the NuTeV sin^2 theta_W anomaly as an application.
We report recent studies of the Asymmetry Analysis Collaboration (AAC) on polarized parton distribution functions (PDFs). Using the data on the spin symmetry A_1 in deep inelastic lepton scattering, we investigate optimum polarized PDFs. Their uncertainties are estimated by the Hessian method. The uncertainties are large for the polarized antiquark and gluon distributions. We discuss the role of accurate SLAC-E155 proton data on the determination of the PDFs. The obtained distributions are compared with other parametrization results.
We report global analysis results of experimental data for nuclear structure-function ratios F_2^A/F_2^{A'} and proton-nucleus Drell-Yan cross-section ratios sigma_{DY}^{pA}/sigma_{DY}^{pA'} in order to determine optimum parton distribution functions (PDFs) in nuclei. An important point of this analysis is to show uncertainties of the distributions by the Hessian method. The results indicate that the uncertainties are large for gluon distributions in the whole x region and for antiquark distributions at x>0.2. We provide a code for calculating any nuclear PDFs at given x and Q^2 for general users. They can be used for calculating high-energy nuclear reactions including neutrino-nucleus interactions, which are discussed at this workshop.
We investigate a possible nuclear correction to the NuTeV measurement of the weak-mixing angle $\sin^2 \theta_W$. In particular, a nuclear modification difference between $u_v$ and $d_v$ distributions contributes to the NuTeV measurement with the iron target. First, the modification difference is determined by a $\chi^2$ analysis so as to reproduce nuclear data on the structure function $F_2$ and Drell-Yan processes. Then, taking the NuTeV kinematics into account, we calculate a contribution to the $\sin^2 \theta_W$ determination. In addition, its uncertainty is estimated by the Hessian method. Although the uncertainty becomes comparable to the NuTeV deviation, the effect is not large enough to explain the whole NuTeV $\sin^2 \theta_W$ anomaly at this stage. However, it is difficult to determine such a nuclear modification difference, so that we need further investigations on the difference and its effect on the NuTeV anomaly.
We investigated a nuclear modification difference between up- and down-valence quark distributions by analyzing structure function F_2 and Drell-Yan cross-section ratios. Although nuclear modifications of the valence-quark distributions themselves are rather well determined, it is difficult to find their difference from the present data. We estimated such an effect on the NuTeV sin^2 theta_W value and its uncertainty by the Hessian method. At this stage, it is not large enough to explain the whole NuTeV anomaly. However, the modification difference cannot be precisely determined, so that further studies are needed.