Dependence of the Form Factors of B to π ell ν on the Heavy Quark Mass

We use QCD sum rules to analyze the semileptonic transition $B \to \pi \ell \nu$ in the limit $m_b \to \infty$. We derive the dependence of the form factor $F_1(0)$ on the heavy quark mass, which is compatible with the expected dependence for the simple pole model of $F_1(q^2)$.