Effects of R-parity violation in unpolarized top quark decay into   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 ${\cal O}(\alpha_s)$ QCD corrections, the ${\cal O}(\alpha)$ electroweak (EW) and finite width corrections, and also the supersymmetric (SUSY) corrections with R-parity conservation, respectively. 
Yi Min Nie, Chong Sheng Li, Qiang Li, Jian Jun Liu and Jun Zhao