Abstract
We calculate the perturbative corrections to order α_s^2β_0 to the sum rule derived from the second moment of the time-ordered product of b \to c currents near zero recoil. This sum rule yields a bound on λ_1, the expectation value of the b quark kinetic energy operator inside the B meson. The perturbative corrections significantly weaken the bound relative to the tree level result, yielding λ_1 < -0.15 GeV^2.
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