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

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arxiv 1004.3417 v3 pith:IHCKDRXN submitted 2010-04-20 hep-th

Bo Feng , Rijun Huang , Yin Jia This is my paper · ORCID
classification hep-th
keywords relationon-shellamplitudegaugeprogramproofrecursions-matrix
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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.

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Cited by 6 Pith papers

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  3. Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter

    hep-th 2026-07 accept novelty 6.0 of 10

    Perturbiner recursion proves color-factor symmetry (hence BCJ relations) for all tree-level YM+matter amplitudes with at least one gluon.

  4. Rational QCD loop amplitudes and quantum theories on twistor space

    hep-th 2024-11 conditional novelty 6.0 of 10

    Twistor-space anomaly cancellation yields linear relations among all-plus and one-minus one-loop QCD gluon subamplitudes, and the number of independent amplitudes is the unsigned Stirling number c(n-1,3) for n up to 8.

  5. UV considerations on scattering amplitudes in a web of theories

    hep-th 2019-08 conditional novelty 6.0 of 10

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    Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.

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