Non-MHV Tree Amplitudes in Gauge Theory

TL;DR

This paper introduces a scalar graph approach to compute all non-MHV tree-level amplitudes in gauge theories, simplifying calculations and ensuring manifest Lorentz and gauge invariance without complex helicity algebra.

Contribution

It presents a novel method using scalar diagrams and a specific reference spinor to directly derive non-MHV amplitudes, avoiding complicated algebraic conversions.

Findings

All non-MHV amplitudes can be obtained from MHV amplitudes using scalar graphs.

Results are free of singularities and manifestly Lorentz and gauge invariant.

The method is illustrated with n-point amplitudes involving three negative helicities.

Abstract

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.