Local infrared safety in time-ordered perturbation theory

TL;DR

This paper introduces a new formulation of time-ordered perturbation theory that ensures infrared safety at the integrand level, enabling numerical evaluation and elimination of unphysical singularities in leptonic annihilation processes.

Contribution

It develops a general expression for weighted cross sections in TOPT, demonstrating local IR divergence cancellation and a reorganized formalism with only physical cuts.

Findings

Infrared divergences cancel locally at the integrand level.

Unphysical singularities in TOPT can be eliminated through reorganization.

The formalism applies to leptonic annihilation, yielding physical unitarity cuts.

Abstract

We develop a general expression for weighted cross sections in leptonic annihilation to hadrons based on time-ordered perturbation theory (TOPT). The analytic behavior of the resulting integrals over spatial momenta can be analyzed in the language of Landau equations and infrared (IR) power counting. For any infrared-safe weight, the cancellation of infrared divergences is implemented locally at the integrand level, and in principle can be evaluated numerically in four dimensions. We go on to show that it is possible to eliminate unphysical singularities that appear in time-ordered perturbation theory for arbitrary amplitudes. This is done by reorganizing TOPT into an equivalent form that combines classes of time orderings into a ``partially time-ordered perturbation theory". Applying the formalism to leptonic annihilation, we show how to derive diagrammatic expressions with only physical unitarity cuts.