Reparametrization invariance constraints on inclusive decay spectra and masses

Reparametrization invariance relations are determined for the inclusive decay spectra of heavy hadrons. They connect the leading-order result to the λ1 term, and the λ2 and ρ2 terms, and imply that the λ1 and ρ2 terms in the total rate occur in the combinations 1+λ1/(2mQ2) and λ2-ρ2/mQ. The relations are satisfied by the known results for the hadronic decay tensors for B→Xc,ulν, B→Xsγ and B→Xsl+l- decays. An interesting field-theory result, the connection between currents in full and effective theories and the change in currents under field redefinitions, is discussed, and is used to determine the effective theory operator whose hadron matrix element is unity to all order in 1/mQ. The hadron masses are given to order ΛQCD3/mQ2 including radiative corrections, and provide an example illustrating the relation between renormalization and reparametrization invariance and μ-independence of 1/mQ3 corrections to physical quantities.