Reparametrization Invariance Constraints on Inclusive Decay Spectra and Masses

TL;DR

This paper derives reparametrization invariance relations for inclusive decay spectra of heavy hadrons, linking various terms in the decay rates and masses, and discusses their implications for theoretical consistency and known decay results.

Contribution

It establishes reparametrization invariance constraints on decay spectra and hadron masses, connecting effective theory currents and providing order (Lambda_QCD)^3/m_Q^2 mass calculations.

Findings

Reparametrization invariance relates decay rate terms involving lambda_1 and lambda_2.

Relations are consistent with known decay tensor results for B decays.

Mass calculations include radiative corrections and demonstrate mu-independence of higher-order terms.

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.