The Subleading Isgur-Wise Form Factor ${\xi }_3(v\cdot v^{\prime })$ and its Implications for the Decays $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$

Abstract

We calculate, in the framework of QCD sum rules and to next-to-leading order in perturbation theory, the universal function ${\xi }_3(v\cdot v^{\prime })$ which appears at order $1/m_Q$ 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, ${\xi }_3(v\cdot v^{\prime })$ is proportional to the leading-order Isgur-Wise function $\xi (v\cdot v^{\prime })$ to very good accuracy. Taking into account all sources of uncertainty, we estimate ${\xi }_3/\xi =(0.6\pm 0.2)$. This reduces the theoretical uncertainty in the extraction of $|V_{cb}|$ from $\bar{B}\to D\ell \bar{\nu }$ transitions. A measurement of the form factor ratio $A_2/A_1$ in $\bar{B}\to D^{\ast }\ell \bar{\nu }$ decays can be used to test our prediction.

14 pages (ReVTeX, 2 figures available), SLAC-PUB-6146, WIS-93/33/May-PH

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