The Subleading Isgur - Wise Form Factor ξ 3 ( v · v ′ ) and its Implications for the Decays B̄ →

We calculate, in the framework of QCD sum rules and to next-to-leading order in perturbation theory, the universal function ξ3(v · v) which appears at order 1/mQ in the heavy quark expansion of meson weak decay form factors. We find that radiative corrections of order αs are very important. Over the kinematic range accessible in semileptonic decays, ξ3(v ·v′) is proportional to the leading-order Isgur-Wise function ξ(v · v) to very good accuracy. Taking into account all sources of uncertainty, we estimate ξ3/ξ = (0.6±0.2). This reduces the theoretical uncertainty in the extraction of |Vcb| from B̄ → D l ν̄ transitions. A measurement of the form factor ratio A2/A1 in B̄ → Dl ν̄ decays can be used to test our prediction.