PERTURBATIVE CORRECTIONS TO ZERO RECOIL INCLUSIVE B-DECAY SUM-RULES

Comparing the result of inserting a complete set of physical states in a time ordered product of b decay currents with the operator produce expansion gives a class of zero recoil sum rules. They sum over physic al states with excitation energies less than Delta, where Delta is muc h greater than the QCD scale and much less than the heavy charm and bo ttom quark masses. These sum rules have been used to derive an upper b ound on the zero recoil limit of the B --> D form-factor, and on the matrix element of the kinetic energy operator between B meson states. Perturbative corrections to the sum rules of order alpha(s)(Delta)Delt a(2)/m(c,b)(2) have previously been computed. We calculate the correct ions of order alpha(s)(Delta) and alpha(s)(2)(Delta)beta(0) keeping al l orders in Delta/m(c,b), and show that these perturbative QCD correct ions suppressed by powers of Delta/m(c,b) significantly weaken the upp er bound on the zero recoil B --> D form-factor, and also on the kine tic energy operator's matrix element.