Non-MHV Tree Amplitudes in Gauge Theory

Details Non-MHV Tree Amplitudes in Gauge Theory Non-MHV Tree Amplitudes in Gauge Theory

2004-07-05

arxiv.org/abs/hep-th/0407027v1

JHEP0407:048,2004

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 6 eps pictures, JHEP class

Scientific paper

10.1088/1126-6708/2004/07/048

We show how all non-MHV tree-level amplitudes in 0 =< N =< 4 gauge theories can be obtained directly from the known MHV amplitudes using the scalar graph approach of Cachazo, Svrcek and Witten. Generic amplitudes are given by sums of inequivalent scalar diagrams with MHV vertices. The novel feature of our method is that after the `Feynman rules' for scalar diagrams are used, together with a particular choice of the reference spinor, no further helicity-spinor algebra is required to convert the results into a numerically usable form. Expressions for all relevant individual diagrams are free of singularities at generic phase space points, and amplitudes are manifestly Lorentz- (and gauge-) invariant. To illustrate the method, we derive expressions for n-point amplitudes with three negative helicities carried by fermions and/or gluons. We also write down a supersymmetric expression based on Nair's supervertex which gives rise to all such amplitudes in 0 =< N =< 4 gauge theories.

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