Power Corrections and KLN Cancellations

We consider perturbative expansions in theories with an infrared cutoff $\lambda$. The infrared sensitive pieces are defined as terms nonanalytic in the infinitesimal $\lambda^2$ and powers of this cutoff characterize the strength of these infrared contributions. It is argued that the sum over the initial and final degenerate ( as $\lambda \to 0$) states which is required by the Kinoshita - Lee - Nauenberg theorem eliminates terms of order $\lambda^0$ and $\lambda^1$. However, the quadratic and higher order terms in general do not cancel. This is investigated in simple examples of KLN cancellations, of relevance to the inclusive decay rate of a heavy particle, at the one loop level.