Perturbative QCD Analysis of B to pi and B to rho Transitions

We calculate the form factors of $B\to\pi$ and $B\to\rho$ heavy to light transition matrix elements by using the factorization formalism of perturbative QCD. We obtain them at $q^2=0$ and show their dependences on the parameter $\epsilon$ of the B meson distribution amplitude. We also obtain the form factors as functions of $q^2$ in the region $0\le q^2 \le M_B^2/2$. The relations among the form factors are found in the limit of $m_\pi /M_B=0$, $m_\rho /M_B=0$, ${M_b/M_B}=1$ and $(1-x)<<1$.