Compact QED Tree-Level Amplitudes From Dressed BCFW Recursion Relations

TL;DR

This paper develops a modified BCFW recursion relation to derive compact tree-level QED amplitudes, significantly reducing complexity growth for multi-photon processes and providing explicit formulas for NMHV and NNMHV cases.

Contribution

It introduces a new recursion relation that simplifies the calculation of QED amplitudes, making complex multi-photon processes more manageable.

Findings

Reduced complexity growth from factorial to exponential

Derived compact formulas for NMHV and NNMHV amplitudes

Demonstrated efficiency of the new recursion relation

Abstract

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and NNMHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.