We calculate, in the framework of QCD sum rules and to next-to-leading order in perturbation theory, the universal function ${\xi }_3\left(v·v^{\prime }\right)$ which appears at order $\frac{1}{m_Q}$ in the heavy quark expansion of meson weak decay form factors. We find that radiative corrections of order ${\alpha }_s$ are very important. Over the kinematic range accessible in semileptonic decays, ${\xi }_3\left(v·v^{\prime }\right)$ is proportional to the leading-order Isgur-Wise function $\xi \left(v·v^{\prime }\right)$ to very good accuracy. Taking into account all sources of uncertainty we estimate $\frac{{\xi }_3}{\xi }=(0.6\mathrm{}\pm 0.2)$. This reduces the theoretical uncertainty in the extraction of $\left|V_{\mathrm{cb}}\right|$ from $\overline{B}\to D\ell \overline{\nu }$ transitions. A measurement of the form factor ratio $\frac{A_2}{A_1}$ in $\overline{B}\to D^{*}\ell \overline{\nu }$ decays can be used to test our prediction.

• Received 24 May 1993

DOI:https://doi.org/10.1103/PhysRevD.49.1302