Transverse momentum dependent factorization for radiative leptonic decay ofB-meson

With a consistent definition of transverse-momentum-dependent(TMD) light-conewave function of $B$-meson, we show that the amplitude of the radiativeleptonic B-decay can be factorized at one-loop level as a convolution with thewave function and a perturbative coefficient function, combined with a softfactor. In this TMD factorization, the transverse momenta of partons in the$B$-meson are taken into account and all soft divergences are contained in thewave function and the soft factor. The coefficient function is infrared-safe.The factorization works on a diagram-by-diagram basis and is possible to extendbeyond one loop. With the factorization the large logarithms in theperturbative function can be simply resummed. Our work shows that the result ofcollinear factorization for the decay can be derived from that of TMDfactorization. Therefore, the two factorizations for the case here are simplyrelated to each other.Comment: 19 pages, 5 figures, typos eliminated, text imporve