Uncertainty in the leading order PQCD calculations of $B$ meson decays

Abstract

Uncertainty in the PQCD calculation of B decays is investigated in $B\to \pi$, $B\to D$ transition form factors and $B\to D\pi$ decay amplitudes. $B$ meson distributionamplitude dependence is studied by taking three kinds of distribution amplitude so far suggested. It is found that almost same $q^2$ dependence of the form factors can be obtained irrespective of the types of the $B$ meson distribution amplitude by suitably choosing one parameter. $B\to D\pi$ process shows the difference due to the distribution amplitude. The effect of the sub-leading component of the $B$ mesondistribution amplitude is also studied in the three processes. The numerical results of calculations with the sub-leading component can be well approximated by the leading order calculation with a suitable choice of the distribution amplitude parameters.

Comments: 21pages, 13 figures; more discussions on RGE scale dependence and 1/M effects are added; typos are corrected