NuTeV $\sin ^2 \theta_{\rm W}$ anomaly and nuclear parton distributions revisited

By studying the Paschos-Wolfenstein (PW) ratio of deep inelastic $\nu{\rm Fe}$ and $\bar \nu{\rm Fe}$ scattering cross sections, we show that it should be possible to explain the NuTeV $\sin ^2 \theta_{\rm W}$ anomaly with quite conventional physics, by introducing mutually different nuclear modifications for the valence-$u$ and valence-$d$ quark distributions of the protons in iron. Keeping the EKS98 nuclear modifications for $u_V+d_V$ as a baseline, we find that some 20-30 % nuclear modifications to the $u_V$ and $d_V$ distributions account for the change induced in the PW ratio by the NuTeV-suggested increase $\Delta \sin ^2 \theta_{\rm W}=0.005$. We show that introduction of such nuclear modifications in $u_V$ and $d_V$ individually, does not lead into contradiction with the present global DGLAP analyses of the nuclear parton distributions, where deep inelastic $lA$ scattering data and Drell-Yan dilepton data from $pA$ collisions are used as constraints. We thus suggest that the NuTeV result serves as an important further constraint in pinning down the nuclear effects of the bound nucleon PDFs. We also predict that if the NuTeV anomaly is explained by this mechanism, the NOMAD experiment should see an increase in the weak mixing angle quite close to the NuTeV result.