Modified perturbation theory for pair production and decay of fundamental unstable particles

TL;DR

This paper develops a new asymptotic expansion method for calculating the cross-section of pair production and decay of unstable particles, effectively handling singularities and applicable up to NNLO order.

Contribution

It introduces a novel perturbation theory approach that manages resonant and kinematic singularities using distribution theory, improving calculations of unstable particle processes.

Findings

The method transforms divergent integrals into convergent ones.

The approach is applicable up to NNLO approximation.

Analysis of the procedure near the production threshold.

Abstract

We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we treat in the sense of distributions. This mode allows us to transform formally divergent integrals into absolutely convergent ones with keeping the asymptotic property of the expansion. The appropriate procedure is elaborated up to an arbitrary order of the expansion. The peculiarity of application of the procedure in the threshold region is analysed. The scheme of the calculations within the NNLO approximation is explicitly discussed.