The systematic study of $B\to \pi$ form factors in pQCD approach and its reliability

Abstract

The study of exclusive B decays in perturbative QCD are complicated by the endpoint problem. In order to perform the perturbative calculation, the Sudakov effects are introduced to regulate the endpoint singularity. We provide a systematic analysis with leading and next-to-leading twist corrections for $B\to \pi$ form factors in pQCD approach. The intrinsic transverse momentum dependence of hadronic wave function and threshold resummation effects are included in pQCD approach. There are two leading twist B meson distribution amplitudes (or generally wave functions) in general. The QCD equations of motion provide important constraints on B meson wave functions. The reliability of pQCD approach in \bpi form factors is discussed. 70% of the result comes from the region ${\alpha }_s(t)/\pi <0.2$ and 38% comes from the region where the momentum transfer $t\geq 1\GeV$. The conceptual problems of pQCD approach are discussed in brief. Our conclusion is that pQCD approach in the present form cannot provide a precise prediction for \bpi transition form factors.

30 pages, latex, some typos corrected, to appear in Nucl. Phys. B

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