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

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 $D\le 6$ 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.

35 pages + appendices + references; 4 figures, 2 tables; journal version