Heavy-meson form factors from QCD sum rules

A consistent framework is developed for studying hadronic form factors of heavy mesons using QCD sum rules in the heavy-quark effective theory, including the next-to-leading-order renormalization-group improvement. Sum rules are derived for the asymptotic value of the meson decay constant $f_P$ and for the universal Isgur-Wise form factor. It is shown that renormalization-group effects considerably enhance the prediction for $f_P$ and bring its asymptotic value in accordance with recent lattice results. Including finite-mass corrections, the dependence of the physical decay constant on the meson mass is investigated. We obtain $f_D\simeq 170\pm 30$ MeV and $f_B\simeq 190\pm 50$ MeV. The origin of the breakdown of the heavy-quark expansion for $f_D$ is analyzed. In the case of heavy-meson transition form factors, both the QCD and $\frac{1}{m_Q}$ corrections are moderate and under control. A sum rule for the renormalized Isgur-Wise function is derived and evaluated. The theoretical result is compared to experimental data.