Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program

TL;DR

This paper uses on-shell recursion relations to prove fundamental gauge amplitude identities within the S-matrix framework, providing a pure field theory proof of the BCJ relation and its physical interpretation.

Contribution

It presents the first pure field theory proof of the BCJ identity using BCFW recursion, reducing the color basis and offering a physical understanding.

Findings

Proved color-order reversed relation, $U(1)$-decoupling, KK, and BCJ relations using BCFW.

First pure field theory proof of the BCJ identity.

Reduced color basis from $(n-2)!$ to $(n-3)!$.

Abstract

Using only the Britto-Cachazo-Feng-Witten(BCFW) on-shell recursion relation we prove color-order reversed relation, $U(1)$-decoupling relation, Kleiss-Kuijf(KK) relation and Bern-Carrasco-Johansson(BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color ordered basis from $(n-2)!$ to $(n-3)!$. Our proof gives also its physical interpretation as the mysterious bonus relation with ${1\over z^2}$ behavior under suitable on-shell deformation for no adjacent pair.