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

TL;DR

This paper develops a unified approach to connect resonant and asymptotic regions in processes with gauge bosons, ensuring gauge invariance and unitarity, exemplified through Higgs-mediated fermion-antifermion to ZZ scattering.

Contribution

It introduces a method to smoothly interpolate between resonant and non-resonant regimes in gauge boson processes while maintaining all fundamental field-theoretical constraints.

Findings

Derived compact expressions for cross-sections

Ensured gauge invariance and unitarity in the approach

Validated the method with Higgs-mediated ZZ production

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 $f\bar{f}\to ZZ$, 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.