Left-right asymmetries in polarized $e-\mu$ scattering

We consider, in the electroweak standard model context, several left-right asymmetries in $\mu e$ elastic scattering at fixed target and collider experiments. For the former case, we show that the muon mass effects are important in a wide energy range. We also show that these asymmetries are sensitive to the electroweak mixing angle ${\theta }_W$. The effect of an extra $Z^{\mathrm{\prime }}$ neutral vector boson appearing in a 331 model is also considered. The capabilities of these asymmetries in the search of this extra $Z^{\mathrm{\prime }}$ are addressed.