The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N} = 2$ Super-QCD

TL;DR

This paper computes the complete two-loop four-gluon scattering amplitude in $ ext{N}=2$ super-QCD, revealing simplified structures in superconformal cases and demonstrating the duality between color and kinematics.

Contribution

It provides the first fully integrated two-loop four-gluon amplitude in $ ext{N}=2$ super-QCD with full dependence on $N_c$ and $N_f$, utilizing a compact integrand with color-kinematics duality.

Findings

Achieved a compact, fully integrated amplitude expression.

Found simplified analytic structures in superconformal case.

Identified the emergence of lower-weight terms compared to $ ext{N}=4$ SYM.

Abstract

We present the fully integrated form of the two-loop four-gluon amplitude in $\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on $N_c$ and $N_f$, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the $\mathcal{N} = 2$ superconformal theory, where $N_f = 2N_c$ , we obtain remarkably simple amplitudes that have an analytic structure close to that of $\mathcal{N} = 4$ super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.