2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198545We consider perturbative expansions in theories with an infrared cutoff $λ$. The infrared sensitive pieces are defined as terms nonanalytic in the infinitesimal $λ^2$ 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 $λ\to 0$) states which is required by the Kinoshita - Lee - Nauenberg theorem eliminates terms of order $λ^0$ and $λ^1$. 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.20 pages, LaTeXHigh Energy Physics - Phenomenologytext