Renormalization-group evolution of the none-local matrix element of B-meson in QCD and B → π transition form factor

Abstract

We consider the renormalization-group evolution of the matrix element of 〈0|q¯(z)β[z,0]b(0)α|B¯〉, which can be used to define the distribution amplitudes for B meson and widely applied in studies of B meson decays. The contribution to the renormalization constant of the non-local operator q¯(z)β[z,0]b(0)α is considered up to one-loop order in QCD. Since the quark fields in this operator are not directly coupled fields, momentum can not flow freely through this non-local operator. Momentum involved in this operator can be treated stringently in coordinate space. We find that the ultraviolet divergences regulated by dimensional parameter ϵ cancel with each other, and the evolution effect vanishes. The matrix element 〈0|q¯(z)β[z,0]b(0)α|B¯〉 escapes from the renormalization-group evolution. We then apply the matrix element in calculating B→π transition form factor, where the matrix element is obtained by using the B meson wave function calculated in QCD-inspired potential model. By comparing with experimental data for the semileptonic decay of B→πℓν and light-cone sum rule calculation, we analyze the perturbative and non-perturbative contributions to B→π transition form factor in the frame work of perturbative QCD approach. We find that the effectiveness of the suppression of Sudakov factor to soft contribution depends on the end-point behavior of B meson wave function, and with the B-meson wave function used in this work, soft contribution can not be well suppressed. The hard contribution to the B→π transition form factor is about 59%, and soft contribution can be as large as 41% in the naive calculation. To make the perturbative calculation reliable, a soft momentum cutoff in the calculation and soft form factor have to be introduced.