Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts

TL;DR

We develop an iterative method to construct four-dimensional generalized unitarity cuts in N=2 SQCD, producing rung-rule–like rules that assemble cuts to all loop orders for four-point, massless MHV amplitudes including external matter. By enforcing color–kinematics duality, we obtain complete four-point two-loop integrands and explore their extensions to external matter, with checks via six-dimensional lifts to capture regularization-dependent pieces. The results demonstrate a chiral, infrared-finite structure in many sectors and reveal close connections to loop-level BCFW-type local integrands, suggesting a path toward higher-loop calculations in QCD-like theories. The work highlights both the power and limitations of color-dual representations in less-than-maximal supersymmetry and points to future directions in three-loop SQCD, non-planar extensions, and deeper IR analyses compatible with dimensional regularization.

Abstract

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For iterated two-particle cuts,specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, reminiscent of the rung rule in $\mathcal{N} = 4$ SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in $\mathcal{N} = 2$ SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in $D\leq 6$ dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral $\mathcal{N} = (1,0)$ SYM as a means of dimensionally regulating loop integrals.

Figures (4)

• Figure 1: The three one-loop masters with mixed external particle content.
• Figure 2: Three two-loop masters with four external vector multiplets.
• Figure 3: The two two-loop masters with external hypermultiplets.
• Figure 4: Two-loop masters with two external vector and matter multiplets.