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The cancellation of infrared (IR) divergences is an old topic in quantumfield theory whose main results are condensed into the celebratedKinoshita-Lee-Nauenberg (KLN) theorem. In this paper, we considermass-suppressed corrections to the leading (i.e. double-logarithmic) IRdivergences in the context of spontaneously broken gauge theories. We work in asimplified theoretical set-up based on the spontaneously broken $U'(1)\otimesU(1)$ gauge group. We analyze, at the one-loop level and includingmass-suppressed terms, the double-logarithmic corrections to the decay channelsof a hypothetical heavy $Z'$ gauge boson coupled to light chiral fermions andmixed with a light massive $Z$ gauge boson. Limited to this theoreticalframework, only final state IR corrections are relevant. We find that fullexploitation of the KLN theorem requires non-trivial combinations of variousdecay channels in order to get rid of the mass-suppressed IR corrections. Basedon this observation we show that, starting from any two-body decay of the heavy$Z'$ gauge boson, the cancellation of the mass-suppressed double-logarithmiccorrections requires the sum over the full decay width (thus enforcing theinclusion of final states which are na\"{\i}vely unrelated to the startingone). En route, we prove a number of technical results that are relevant forthe computation of mass-suppressed double-logarithms of IR origin. Our resultsare relevant for models that enlarge the Standard Model by adding a heavy $Z'$.

Power suppressed corrections show new features of infrared cancellations