Nuclear modification difference between u_v and d_v distributions and its relation to NuTeV sin^2 theta_W anomaly

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 differenceis 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.