MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop

TL;DR

This paper calculates one-loop MHV amplitudes in N=2 SQCD with all external particles in the adjoint representation, comparing them to N=4 SYM, and explores potential higher-order factorization properties in superconformal theories.

Contribution

It extends the calculation of one-loop MHV amplitudes to N=2 SQCD with fundamental flavors and investigates their relation to N=4 SYM amplitudes, especially in the conformal case.

Findings

In N=4 SYM, MHV amplitudes are proportional to tree-level results.

In N=2 SQCD, MHV amplitudes differ from N=4 except at conformal point where N_f=2N_c.

At the conformal point, N=2 MHV amplitudes match N=4 results.

Abstract

Using four-dimensional unitarity and MHV-rules we calculate the one-loop MHV amplitudes with all external particles in the adjoint representation for N=2 supersymmetric QCD with N_f fundamental flavours. We start by considering such amplitudes in the superconformal N=4 gauge theory where the N=4 supersymmetric Ward identities (SWI) guarantee that all MHV amplitudes for all types of external particles are given by the corresponding tree-level result times a universal helicity- and particle-type-independent contribution. In N=2 SQCD the MHV amplitudes differ from those for N=4 for general values of N_f and N_c. However, for N_f=2N_c where the N=2 SQCD is conformal, the N=2 MHV amplitudes (with all external particles in the adjoint representation) are identical to the N=4results. This factorisation at one-loop motivates us to pose a question if there may be a BDS-like factorisation for these amplitudes which also holds at higher orders of perturbation theory in superconformal N=2 theory.