  We perform perturbative QCD factorization of infrared radiations associated
with an energetic $b$ quark from a polarized top quark decay, taking the
semi-leptonic channel as an example. The resultant formula is expressed as a
convolution of an infrared-finite heavy-quark kernel with a $b$-quark jet
function. Evaluating the heavy-quark kernel up to leading order in the coupling
constant and adopting the jet function from QCD resummation, we predict the
dependence of the spin analyzing power for a polarized top quark on the
invariant mass of the $b$-quark jet. It is observed that the spin analyzing
power could be enhanced by a factor 2 compared to the inclusive case with the
jet mass being integrated over. It is worthwhile to test experimentally the
enhancement of the spin analyzing power due to the inclusion of jet dynamics.
