$B$ meson wave function in $k_T$ factorization

Abstract

We study the asymptotic behavior of the $B$ meson wave function in the framework of $k_T$ factorization theorem. We first construct a definition of the $k_T$-dependent $B$ meson wave function, which is free of light-cone divergences. Next-to-leading-order corrections are then calculated based on this definition. The treatment of different types of logarithms in the above corrections, including the Sudakov logarithms, and those depending on a renormalization scale and on an infrared regulator, is summarized. The criticism raised in the literature on our resummation formalism and Sudakov effect is responded. We show that the $B$ meson wave function remains normalizable after taking into account renormalization-group evolution effects, contrary to the observation derived in the collinear factorization theorem.