New directions for top quark polarization in the $t$-channel process

We define three orthogonal axes to investigate the top quark polarization in the $t$-channel single top process. We provide expressions for the polarization in these axes in terms of anomalous $Wtb$ couplings. It is found that the polarizations in the two axes orthogonal to the spectator quark axis are very sensitive to an anomalous coupling involving a $\bar b_L \sigma^{\mu \nu} t_R$ dipole term. In particular, an asymmetry based on the polarization normal to the production plane is more sensitive to the imaginary part of this coupling than previously studied observables.