Inconsistences of the k_T-Factorization in Exclusive B-Meson Decays

The k_T-factorization has been widely used for exclusive decays of B-mesons. In this factorization the pertubative coefficients are extracted from scattering of off-shell partons. Because the off-shellness of partons the extracted pertubative coefficients in general are not gauge-invariant. We show that these perturbative coefficients contain gauge-dependent singularities beyond tree-level. This leads to that the k_T-factorization is gauge-dependent and violated in the general covariant gauge. This is not consistent with expectations of physics. In the factorization there exist two different wave functions for a B-meson in general. We show that the two wave functions satisfy different evolution equations whose solutions are used to re-sum large log's. Based on this fact, the rseummation of large log's at leading log approximation in the widely used k_T-factorization with only one wave function is inconsistent.