The Pure Leptonic Decays of $D_s$ Meson and Their Radiative Corrections

Abstract

The radiative corrections to the pure leptonic decay $D_s⟶\ell {\nu }_{\ell }$ up-to one-loop order is presented. We find the virtual photon loop corrections to $D_s⟶\tau {\nu }_{\tau }$ is negative and the corresponding branching ratio is larger than $3.51\times 10^{-3}$. Considering the possible experimental resolutions, our prediction of the radiative decay $D_s⟶\tau {\nu }_{\tau }\gamma$ is not so large as others, and the best channel to determine the $V_{cs}$ or $f_{D_s}$ is $D_s⟶\mu {\nu }_{\mu }\gamma$. How to cancel the infrared divergences appearing in the loop calculations, and the radiative decay $D_s⟶\ell {\nu }_{\ell }\gamma$ is shown precisely. It is emphasized that the radiative decay may be separated properly and may compare with measurements directly as long as the theoretical `softness' of the photon corresponds to the experimental resolutions.

Comments: 11 pages, 1 Latex file, 8 ps figures