Electroweak and finite width corrections to top quark decays into transverse and longitudinal W -bosons

We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a $ W $-gauge boson where the helicities of the $ W $ are specified as longitudinal, transverse-plus and transverse-minus. Together with the $ O(\alpha_s) $ corrections these corrections may become relevant for the determination of the mass of the top quark through angular decay measurements.