Perturbative QCD corrections to inclusive lepton distributions from semileptonic $b \to c\tau\bar\nu_\tau$ decays

Perturbative corrections of the order of $\alpha_s$ to inclusive double differential lepton distribution from $b$ quark decay are considered. A perturbative correction to the charged lepton energy spectrum has been calculated for an arbitrary charged lepton mass. The perturbative contribution suppresses the partial rate but almost does not change the shape of energy distribution. Applications of our result to semileptonic B meson decays are briefly discussed.