N=4 SYM NMHV Loop Amplitude in Superspace

TL;DR

This paper constructs a full superspace form of the 6-point NMHV loop amplitude in N=4 Super Yang-Mills theory, enabling simplified calculations of various particle scattering processes.

Contribution

It introduces a comprehensive superspace formulation for the 6-point NMHV loop amplitude in N=4 SYM, facilitating easier derivation of different external particle configurations.

Findings

Verified amplitudes with two gluinos match previous calculations

Provided explicit results for gluino and scalar scattering amplitudes

Discussed MHV vertex approach for simplifying loop amplitude computations

Abstract

Here we construct N=4 SuperYang-Mills 6 point NMHV loop amplitude (amplitudes with three minus helicities) as a full superspace form, using the $SU(4)_{R}$ anti-commuting spinor variables. Amplitudes with different external particle and cyclic helicity ordering are then just a particular expansion of this fermionic variable. We've verified this by explicit expansion obtaining amplitudes with two gluino calculated before. We give results for all gluino $A(\Lambda^{-}\Lambda^{-}\Lambda^{-}\Lambda^{+}\Lambda^{+}\Lambda^{+})$and all scalar $A(\phi\phi\phi\phi\phi\phi)$scattering amplitude. A discussion of using MHV vertex approach to obtain these amplitudes are given, which implies a simplification for general loop amplitudes.