Comment on the Renormalization Group Improvement in Exclusive $b\ra c $ Transitions

Abstract

Using rather general consideration I argue that the numerical impact of the existing next-to-leading logarithmic summations of terms $\log{m_b/m_c}$ for perturbative factors $η_A$, $η_V$ in the exclusive zero recoil semileptonic transitions is irrelevant, and adopting corresponding corrections beyond the exact one loop result for both estimating the values of these formfactors and their theoretical uncertainty, is misleading. The central theoretical value if taken literally is then $η_A\simeq 0.97$.