Pure leptonic decays of the Bc meson and their radiative corrections

The one-loop radiative corrections to the pure leptonic decay B_c-->lν_l are presented. We treat the infrared divergences appearing in the loop calculations together with those in the radiative decay B_c-->lν_lγ. The divergences are finally canceled by each other to make the results finite. It is emphasized that the radiative decay may be separated properly from the pure leptonic decays. We can compare our results with the experimental measurements directly as long as the theoretical ``softness'' of the photon corresponds to the experimental resolutions. Furthermore with the nonrelativistic constituent quark model, the typical long distance contributions to the radiative decays are estimated, and it is shown that the contributions are negligible in comparison with the accuracy of one-loop corrections and the expected experimental measurements.