Modified Paschos-Wolfenstein relation and extraction of the weak mixing anglesin2θW

The NuTeV Collaboration reported an anomalously large weak mixing angle ${\sin }^2{\theta }_W$ in comparison with the standard model prediction. Neutrino and antineutrino charged- and neutral-current events are analyzed for extracting ${\sin }^2{\theta }_W.$ Although the Paschos-Wolfenstein relation is not directly used in the analysis, it plays an important role in the determination. Noting that the target nucleus, iron, is not an isoscalar nucleus, we derive a leading-order expression for a modified Paschos-Wolfenstein relation for nuclei, which may have neutron excess. Then, using charge and baryon-number conservations for nuclei, we discuss a nuclear correction in the ${\sin }^2{\theta }_W$ determination. It is noteworthy that nuclear modifications are different between valence up- and down-quark distributions. We show this difference effect on the NuTeV ${\sin }^2{\theta }_W$ deviation.