Transverse momentum dependent light-cone wave function of B-meson and relation to the momentum integrated one

A direct generalization of the transverse momentum integrated (TMI) light-cone wave function to define a transverse momentum dependent (TMD) light-cone wave function will cause light-cone singularities and they spoil TMD factorization. We motivate a definition in which the light-cone singularities are regularized with non-light like Wilson lines. The defined TMD light-cone wave function has some interesting relations to the corresponding TMI one. When the transverse momentum is very large, the TMD light-cone wave function is determined perturbatively in term of the TMI one. In the impact b-space with a small b, the TMD light-cone wave function can be factorized in terms of the TMI one. In this Letter we study these relations. By-products of our study are the renormalization evolution of the TMI light-cone wave function and the Collins-Soper equation of the TMD light-cone wave function, the later will be useful for resumming Sudakov logarithms.