Effects of R-parity violation in unpolarized top quark decay into a polarized W boson

We calculate one-loop R-parity violating corrections to the top quark decay into a bottom quark and a polarized W-gauge boson. The corrections are presented according to the total corrections, the longitudinal corrections and the transverse corrections, respectively. We compared our results with the $\mathcal{O}({\alpha }_s)$ QCD corrections, the $\mathcal{O}(\alpha )$ electroweak (EW) and finite width corrections, and also the supersymmetric (SUSY) corrections with R-parity conservation, respectively.