Radiative corrections to $b\to c\tau \text{bat}{\nu }_{\tau }$

Analytical calculation is presented of the QCD radiative corrections to the rate of the process $b\to c\tau {\bar{\nu }}_{\tau }$ and to the $\tau$ lepton longitudinal polarization in $\tau {\bar{\nu }}_{\tau }$ rest frame. The results are given in the form of one dimensional infrared finite integrals over the invariant mass of the leptons. We argue that this form may be optimal for phenomelogical applications due to a possible breakdown of semilocal hadron-parton duality in decays of heavy flavours.