Consistent Analysis of the $B\to \pi$ Transition Form Factor in the Whole Physical Region

Abstract

In the paper, we show that the $B\to \pi$ transition form factor can be calculated by using the different approach in the different $q^2$ regions and they are consistent with each other in the whole physical region. For the $B\to \pi$ transition form factor in the large recoil regions, one can apply the PQCD approach, where the transverse momentum dependence for both the hard scattering part and the non-perturbative wavefunction, 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 wavefunction for ${\Psi }_p$ and we find that its contribution is less than the leading twist contribution. Both the two wavefunctions ${\Psi }_B$ and ${\bar{\Psi }}_B$ of the B meson can give sizable contributions to the $B\to \pi$ 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.

18pages, 6 figures

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