Factorization of radiative leptonic decays of B− and D− mesons including the soft photon region

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(ΛQCD/mQ). We consider the contribution in the soft photon region that Eγ∼ΛQCD2/mQ. The numerical results show that, the soft photon region is very important for both the B and D mesons. The branching ratios of B→γeνe is 5.21×10−6, which is about 3 times of the result obtained by only considering the hard photon region Eγ∼mQ. And for the case of D→γeνe, the result of the branching ratio is 1.92×10−5.