Power suppressed corrections show new features of infrared cancellations

TL;DR

This paper investigates how mass-suppressed infrared corrections in spontaneously broken gauge theories affect IR divergence cancellations, revealing that full decay width summation is necessary for proper IR divergence cancellation.

Contribution

It demonstrates that mass-suppressed IR corrections require summing over all decay channels for IR divergence cancellation, extending the understanding of the KLN theorem in broken gauge theories.

Findings

Mass-suppressed double-logarithmic IR corrections require full decay width summation.

IR divergence cancellation involves non-trivial combinations of decay channels.

Technical results for computing mass-suppressed IR double-logarithms are established.

Abstract

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