Corrections to the Bjorken and Voloshin sum rules

We calculate near zero recoil the order αs corrections to the Bjorken and Voloshin sum rules that bound the B → D(∗) l ν̄ form factors. These bounds are derived by relating the result of inserting a complete set of physical states in a time ordered product of weak currents to the operator product expansion. The sum rules sum over physical states with excitation energies less than a scale ∆. We find that the corrections to the Bjorken bound are moderate, while the Voloshin bound receives sizable corrections enhanced by ∆/ΛQCD. With some assumptions, we find that the slope parameter for the form factor hA1 in B → D l ν̄ decay satisfies 0.4 ∼ ρ2A1 ∼ 1.3.