Reparametrization invariance and partial re-summations of the heavy quark expansion

Abstract

We extend existing work on reparametrization invariance (RPI) of the heavy-quark expansion (HQE). RPI implies relations between different orders of the HQE. We discuss the total rates of inclusive processes and obtain results which have a manifest RPI and can be expressed through matrix elements of operators and states defined in full QCD. This approach leads to a partial re-summation of higher-order terms in the heavy-quark expansion. It has the advantage that for reparametrization-invariant observables it shows that the number of independent non-perturbative parameters can be reduced.