Perturbative corrections to the semileptonic b-decay moments:: Elcut dependence and running-α8 effects in the OPE approach

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)) axe 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-l, decreasing the moments at higher cuts. The hardness of hadronic moments is quantitatively illustrated for different cuts on E-l.