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The Subleading Isgur-Wise Form Factor $ξ_3(v\cdot v')$ and its Implications for the Decays $\bar B\to D^{(*)}\ell\,\barν$

We calculate, in the framework of QCD sum rules and to next-to-leading order in perturbation theory, the universal function $ξ_3(v\cdot v')$ 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 $α_s$ are very important. Over the kinematic range accessible in semileptonic decays, $ξ_3(v\cdot v')$ is proportional to the leading-order Isgur-Wise function $ξ(v\cdot v')$ to very good accuracy. Taking into account all sources of uncertainty, we estimate $ξ_3/ξ=(0.6\pm 0.2)$. This reduces the theoretical uncertainty in the extraction of $|\,V_{cb}|$ from $\bar B\to D\,\ell\, \barν$ transitions. A measurement of the form factor ratio $A_2/A_1$ in $\bar B\to D^*\ell\,\barν$ decays can be used to test our prediction.