Scattering amplitudes from a deconstruction of Feynman diagrams

TL;DR

This paper introduces a method to compute scattering amplitudes by decomposing Feynman diagrams into on-shell subamplitudes using BCFW recursion and the Feynman-tree theorem, offering an on-shell, gauge-invariant approach.

Contribution

It presents a novel technique combining BCFW recursion and the Feynman-tree theorem to deconstruct Feynman diagrams into on-shell subamplitudes for scattering amplitude calculations.

Findings

All Feynman diagrams can be expressed in terms of on-shell subamplitudes.

Each cut from the Feynman-tree theorem corresponds to phase space integration of unobserved particles.

The method provides an alternative, gauge-invariant way to compute scattering amplitudes.

Abstract

We show how to apply the BCFW recursion relation to Feynman loop integrals with the help of the Feynman-tree theorem. We deconstruct in this way all Feynman diagrams in terms of on-shell subamplitudes. Every cut originating from the Feynman-tree theorem corresponds to an integration over the phase space of an unobserved particle pair. We argue that we can calculate scattering amplitudes alternatively by the construction of on-shell and gauge-invariant subamplitudes.