Reparametrization Invariance Constraints on Inclusive Decay Spectra and Masses

Abstract

Reparametrization invariance relations are determined for the inclusive decay spectra of heavy hadrons. They connect the leading order result to the lambda_1 term, and the lambda_2 and rho_2 terms, and imply that the lambda_1 and rho_2 terms in the total rate occur in the combinations 1+lambda_1/(2m_Q^2) and lambda_2-rho_2/m_Q. The relations are satisfied by the known results for the hadronic decay tensors for B -> X e nu, B -> X gamma and B -> X e+ e- 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. The hadron masses are given to order (Lambda_QCD)^3/m_Q^2 including radiative corrections, and provide an example illustrating the relation between renormalization and reparametrization invariance and mu-independence of 1/m_Q^3 corrections to physical quantities.