Lepton transverse polarization in the B --> D l nu_l decay due to the electromagnetic final state interaction

The effect of lepton transverse polarization in the B^0 --> D^- l^+ nu_l, B^+ --> bar(D^0) l^+ nu_l decays (l= tau, mu) is analyzed within the framework of Standard Model in the leading order of HQET. It is shown that the non-zero transverse polarization appears due to the electromagnetic final state interaction. The diagrams with intermediate D, D^* - mesons contributing to the non-vanishing P_T are considered. Regarding only the contribution of these mesons, values of the tau-lepton transverse polarization, averaged over the physical region, in the B^0 --> D^- tau^+ nu_l and B^+ --> bar(D^0) tau^+ nu_l decays are equal to $2.60 cdot 10^{-3} and -1.59 cdot 10^{-3}, correspondingly. In the case of muon decay modes the values of <P_T> are equal to 2.97 cdot 10^{-4} and -6.79 cdot 10^{-4}.