Factorization of Radiative Leptonic Decays of $B^{-}$ and $D^{-}$ Mesons Including the Soft Photon Region

Abstract

In this work, we study the radiative leptonic decays of $B^{-}$ and $D^{-}$ mesons using factorization approach. Factorization is proved to be valid explicitly at 1-loop level at any order of $O({\Lambda }_{\mathrm{QCD}}/m_Q)$. We consider the contribution in the soft photon region that $E_{\gamma }\sim {\Lambda }_{\mathrm{QCD}}^2/m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to \gamma e{\nu }_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma }\sim m_Q$. And for the case of $D\to \gamma e{\nu }_e$, the result of the branching ratio is $1.92\times 10^{-5}$.

Comments: arXiv admin note: text overlap with arXiv:1409.0358