Factorization of Radiative Leptonic Decays of $B^{-}$ and $D^{-}$ Mesons

Abstract

In this work, we study the factorization of the radiative leptonic decays of $B^{-}$ and $D^{-}$ mesons, the contributions of the order $O({\Lambda }_{\mathrm{QCD}}/m_Q)$ are taken into account. The factorization is proved to be valid explicitly at the order $O({\alpha }_s{\Lambda }_{\mathrm{QCD}}/m_Q)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O({\Lambda }_{\mathrm{QCD}}/m_Q)$ contribution is found to be very important, the correction to the decay amplitudes of $B^{-}\to \gamma e\bar{\nu }$ is about $20\%-30\%$. For $D$ mesons, the $O({\Lambda }_{\mathrm{QCD}}/m_Q)$ contributions are more important.

Comments: 26 pages, 8 figures. Version to appear in Nucl. Phys. B