Perturbative corrections to the semileptonic b-decay moments: E^\ell_{cut} dependence and running-\alpha_s effects in the OPE approach

Abstract

We have calculated the perturbative corrections to all the structure functions in the semileptonic decays of a heavy quark. Assuming an arbitrary gluon mass as a technical tool allowed to obtain in parallel all the BLM corrections. We report the basic applications, viz. perturbative corrections to the hadronic mass and energy moments with full dependence on the charge lepton energy cut. In the adopted scheme with the OPE momentum scale separation around 1 GeV the perturbative corrections to <M_X^2> are small and practically independent of E_{cut}; the BLM corrections are small, too. The corrections to the second mass squared moment show some decrease with E_{cut} consistent with the effect of the Darwin operator, within the previously estimated theoretical uncertainty. Perturbative corrections in the pole-type schemes appear significant and vary with E_\ell, decreasing the moments at higher cuts. The hardness of hadronic moments is quantitatively illustrated for different cuts on E_\ell.