Asymptotic properties of Born-improved amplitudes with gauge bosons in the final state

Abstract

For processes with gauge bosons in the final state we show how to continuously connect with a single Born-improved amplitude the resonant region, where resummation effects are important, with the asymptotic region far away from the resonance, where the amplitude must reduce to its tree-level form. While doing so all known field-theoretical constraints are respected, most notably gauge invariance, unitarity and the equivalence theorem. The calculations presented are based on the process $f\overline{f}\ensuremath{\rightarrow}ZZ,$ mediated by a possibly resonant Higgs boson; this process captures all the essential features, and can serve as a prototype for a variety of similar calculations. By virtue of massive cancellations the resulting closed expressions for the differential and total cross sections are particularly compact.