Perturbative corrections to a sum rule for the heavy quark kinetic energy

We calculate the perturbative corrections to order αs2β0 to the sum rule derived from the second moment of the time-ordered product of b → c currents near zero recoil. This sum rule yields a bound on λ1, 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 λ1 < −0.15 GeV2.