Application of the Feynman-tree theorem together with BCFW recursion relations

TL;DR

This paper demonstrates how combining the Feynman-tree theorem with BCFW recursion relations allows for constructing on-shell, gauge-invariant amplitudes, specifically applied to electron-photon vertex corrections, matching traditional loop calculations.

Contribution

It applies the combined method to a specific quantum electrodynamics correction, providing explicit phase-space integrals and validating the approach against conventional results.

Findings

Sum of amplitudes matches traditional loop calculation

Explicit phase-space integrals provided for vertex correction

Method extends on-shell amplitude construction to loop corrections

Abstract

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.