Eur. Phys. J. C (2006) 46: 741-750
https://doi.org/10.1140/epjc/s2006-02484-y

Theoretical Physics

Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD

¹ Physics Department, Nuclear & Particle Physics Section, University of Athens, 15771, Athens, Greece
² IMAPP, Institute of Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands
³ Institute of Nuclear Physics, NCSR “Demokritos”, 15310, Athens, Greece

^* e-mail: pdrag@phys.uoa.gr

Received: 1 December 2005
Published online: 31 March 2006

Abstract

We present a proof of the Britto–Cachazo–Feng–Witten tree-level recursion relation for gluon amplitudes in QCD, based on a direct equivalence between BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence can be made explicit when working in a convenient gauge. We exhibit that gauge invariance and the particular structure of Yang–Mills vertices guarantee the validity of the BCFW construction.