A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory

Details A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory

2010-12-29

arxiv.org/abs/1101.0009v1

JHEP 1102:112,2011

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, no figure

Scientific paper

10.1007/JHEP02(2011)112

In last couple years, an important relation (BCJ relation) between color-ordered tree-level scattering amplitudes of gauge theory has inspired many studies. This relation implies that the minimal basis for the color-ordered tree-level amplitudes is $(n-3)!$ and other amplitudes can be expanded into a particular chosen basis. In this paper we will prove the conjectured explicit minimal basis expansion. For this purpose we will write down general BCJ relation of gauge theory by taking the field theory limit of BCJ relation in string theory. Then we prove these general BCJ relations using BCFW on-shell recursion relation. Using these general BCJ relations, we prove the conjectured explicit minimal-basis expansion of gauge theory tree amplitudes inductively.

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