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

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

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