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Two-loop \( \mathcal{N}=2 \) SQCD amplitudes with external matter from iterated cuts. (English) Zbl 1418.81087

Summary: 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.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
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