Alternative Treatment of the Quark Mass in the Heavy Quark Expansion

The treatment of the quark mass plays an important role when it comes to increasing the precision of the predictions of the heavy quark expansion for inclusive heavy hadron decays. Various short-distance mass schemes have been invented to minimize the uncertainties induced by the quark mass, which needs to be extracted from other, independent observables. We suggest to replace the quark mass directly by an observable such as e.g. the inverse moments of the cross section for $e^+ e^- \to $ hadrons. We investigate this alternative strategy and study its impact on the perturbative series.