Consistent analysis of the B→π transition form factor in the whole physical region

In this paper, we show that the B→π transition form factor can be calculated by using the different approach in the different q2 regions and they are consistent with each other in the whole physical region. For the B→π transition form factor in the large recoil regions, one can apply the perturbative quantum chromodynamics (PQCD) approach, where the transverse momentum dependence for both the hard-scattering part and the nonperturbative wave function, the Sudakov effects and the threshold effects are included to regulate the endpoint singularity and to derive a more reliable PQCD result. Pionic twist-3 contributions are carefully studied with a better endpoint behavior wave function for Ψp and we find that its contribution is less than the leading twist contribution. Both the two wave functions ΨB and ΨB of the B meson can give sizable contributions to the B→π transition form factor and should be kept for a better understanding of the B decays. The present obtained PQCD results can match with both the QCD light cone sum rule results and the extrapolated lattice QCD results in the large recoil regions