Cancellation of $1/m_Q$ Corrections to the Inclusive Decay Width of a Heavy Quark

Abstract

We consider the infrared sensitivity of the inclusive heavy quark decay width in perturbation theory. It is shown by explicit calculations to the second loop order (when the non-abelian nature of the QCD interactions first become apparent) that all infrared sensitive terms to logarithmic and linear accuracy cancel when the decay width is expressed in terms of the short distance mass. This in turn implies the absense of any non perturbative $1/m_Q$ power corrections to the decay width. The cancellation is shown algebraically at the level of the Feynman integrands without any use of an explicit infrared cutoff. This result is in accord with the implications of the KLN theorem.