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 1z2 behavior under suitable on-shell deformation for no adjacent pair.
Highlights
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
S-matrix program[1] is a program to understand the scattering amplitude of quantum field theory based only on some general principles, like the Lorentz invariance, Locality, Causality, Gauge symmetry as well as Analytic property. The significance of this approach is its generality: results so obtained do not rely on any detail information of theories, such as the Lagrangian description of theories
One big step along S-matrix program is the unitarity cut method proposed in [2], where on-shell tree amplitudes have been applied to the calculation of loop amwell known fundamental facts in S
Summary
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. Property (4) is conjectured through the Jacobi-As reader will see, what we do in whole paper is to use (1) to identity but has only been proved from string theory [9] (see expand, recombine and reshuffle different amplitude com- further study [10]). The importance of BCJ and KLT relations lies in the mysterious observation: on-shell gravity likes the square of gauge theory while their off-shell Lagrangian descriptions are completely different (one is normalizable and another one, unnormalizable).
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