Perturbative QCD analysis of B to π and B to ρ transitions

Abstract.

We calculate the form factors $F_0$ and $F_1$ of $B\rightarrow\pi$ and V, $A_0$, $A_1$ and $A_2$ of $B\rightarrow\rho$ transition matrix elements by using the factorization formalism of perturbative QCD in the region $0\le q^2 \le M_B^2/2$. In the limit of $m_\pi /M_B=0$, $m_\rho /M_B=0$, ${M_b/M_B}=1$ and $(1-x)\ll 1$, the results show that $F_0$ and $A_1$ are of monopole type, V, $A_0$ and $A_2$ of dipole type, and $F_1$ of a combination of monopole and dipole types with dipole type dominating.