Amplitude for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Gluon Scattering

Parke, Stephen J.; Taylor, Tomasz R.

doi:10.1103/physrevlett.56.2459

Cited by 864 publications

(1,381 citation statements)

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“…6 This and all statements about the general structure of Feynman diagrams can be easily derived from the lagrangian density L = √ −gR with gµν = ηµν + hµν .…”

Section: Outline Of the Proofmentioning

confidence: 99%

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Taming tree amplitudes in general relativity

Benincasa

Boucher-Veronneau

Cachazo

2007

J. High Energy Phys.

164

260

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Abstract:We give a proof of BCFW recursion relations for all tree-level amplitudes of gravitons in General Relativity. The proof follows the same basic steps as in the BCFW construction and it is an extension of the one given for next-to-MHV amplitudes by one of the authors and P. Svrček in hep-th/0502160. The main obstacle to overcome is to prove that deformed graviton amplitudes vanish as the complex variable parameterizing the deformation is taken to infinity. This step is done by first proving an auxiliary recursion relation where the vanishing at infinity follows directly from a Feynman diagram analysis. The auxiliary recursion relation gives rise to a representation of gravity amplitudes where the vanishing under the BCFW deformation can be directly proven. Since all our steps are based only on Feynman diagrams, our proof completely establishes the validity of BCFW recursion relations. This means that results in the literature that were derived assuming their validity become true statements.

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“…6 This and all statements about the general structure of Feynman diagrams can be easily derived from the lagrangian density L = √ −gR with gµν = ηµν + hµν .…”

Section: Outline Of the Proofmentioning

confidence: 99%

“…Many analytic formulas were found or proven by using the Berends-Giele recursion relations introduced in the 80's [1,2,3,4,5]. One important example are the wonderfully simple formulas conjectured by Parke-Taylor [6] for MHV (Maximally Helicity Violating) tree level amplitudes of gluons.…”

Section: Introductionmentioning

confidence: 99%

Taming tree amplitudes in general relativity

Benincasa

Boucher-Veronneau

Cachazo

2007

J. High Energy Phys.

164

260

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“…Using the colour decomposition (2.1) in the helicity formalism [24], we note that there is only one independent colour-stripped tree sub-amplitude, the Parke-Taylor sub-amplitude [25]. Using the spinor products in the limit s ≫ |u| (which can be easily derived from the amplitudes listed in the appendix of Ref.…”

Section: Quark-gluon Amplitudes At Tree and One-loop Levelmentioning

confidence: 99%

The quark Regge trajectory at two loops

Bogdan

Fadin

Duca

et al. 2002

J. High Energy Phys.

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The hypothesis of the quark Reggeization is tested by taking the high-energy limit of the two-loop amplitude for quark-gluon scattering which was recently calculated. The limit is compatible with the Reggeization in the leading and the next-to-leading orders and allows the determination of the quark trajectory in the two-loop approximation. The trajectory is presented as an expansion in powers of (D − 4) for the space-time dimension D tending to the physical value D = 4.

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“…A tree n is the familiar Parke-Taylor tree level MHV amplitude [9], which contains the information about the helicities, while V n is a universal one-loop function independent of which two gluons have negative helicity. 3 Because A tree n is a holomorphic function of positive chirality spinor variables λ i , i = 1, .…”

Section: Jhep10(2004)074mentioning

confidence: 99%