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A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
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abstract
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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Cited by 1 Pith paper
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Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
Perturbiner recursion proves color-factor symmetry (hence BCJ relations) for all tree-level YM+matter amplitudes with at least one gluon.
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