New recursion relations for tree amplitudes of gluons

By R. Britto, F. Cachazo, Bo Feng. 2004

1,082 citations recorded by the source corpus.

Abstract We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A ( 1 + , 2 − , 3 + , 4 − , 5 + , 6 − , 7 + , 8 − ) . We show how to build any amplitude in terms of three-gluon amplitudes only.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e3c1cefb2ffef340db1d0f0f1c015947e63a4a79

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In Nuclear and High Energy Physics

1. C. Cheung
2. F. Cachazo
3. N. Arkani-Hamed
4. S. Caron-Huot
5. L. Mason
6. Pierpaolo Mastrolia
7. L. Alday
8. J. Trnka

Citations in the corpus

• MadGraph 5: going beyond (2011, methodology): “Beyond 7 gluons, explicitly calculating the amplitude associated with each Feynman diagram is not viable and recursive relations need to be employed [60, 61].”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “Of course by now we have become accustomed to the idea that amplitudes can be ‘determined’ using on-shell data—as evidenced, for instance, by the BCFW recursion relations at tree-, [72,73], and loop-levels, [13] (see also [74–77]).”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, methodology): “This inspired the development of recursive techniques to construct tree-level gauge theory amplitudes known as the BCFW recursion relations [15, 16].”
• Supersymmetric gauge theories in twistor space (2006, background): “Nonetheless, we will conclude by 1The recursion relations of Britto, Cachazo & Feng [10], though even more succinct, are of less relevance for this paper; they are closer to the theory in ambitwistor space [11].”
• Direct proof of the tree-level scattering amplitude recursion relation in Yang-mills theory. (2005, methodology): “Among other things, a new set of recursion relations for computing tree-level amplitudes of gluons has recently been introduced [1].”
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators (2012, methodology): “More recently, starting with the development of the BCFW recursion relations [5], there has been rapid progress in the development of new on-shell techniques to compute amplitudes without using Feynman diagrams at all.”
• Integrand reduction of one-loop scattering amplitudes through Laurent series expansion (2012, methodology): “Introduction The recent development of novel methods for computing one-loop scattering amplitudes has been highly stimulated by a deeper understanding of their multi-channel factorization properties under special kinematics enforced by on-shellness [1, 2] and generalized unitarity [3, 4].”
• Direct extraction of one loop rational terms (2008, neutral): “Keywords: QCD, Hadron Colliders.”
• Cut-constructible part of QCD amplitudes (2006, neutral): “(ℓ + 2 ,2 −,3+,4−,5+,ℓ− 1 ) +A(ℓ− 1 ,6 +,1−,ℓ+ 2 )A(ℓ − 2 ,2 −,3+,4−,5+,ℓ+ 1 ) i = − 2h1ℓ1i2h1ℓ2ih42i4[5ℓ1][5ℓ2]2 h23ih34ih61ih6ℓ1ihℓ2 ℓ1ih2|P234|5]h4|P234|ℓ2][ℓ1 ℓ2](P2 234) + 2h1ℓ1i2h1ℓ2ih2ℓ1i2h2ℓ2i[35]4 h61ih6ℓ1ihℓ1 ℓ2ihℓ2 ℓ1ih2|Pℓ 1ℓ22|5]hℓ1|Pℓ 1ℓ22|3][34][45](P 2 ℓ1ℓ22 ) − 2h1ℓ1i2h1ℓ2ih4ℓ1i2h4|”