Abstract
We compute four-point scattering amplitudes in $$ \mathcal{N}=2 $$ SCQCD with general external matter configurations using $$ \mathcal{N}=1 $$ superspace Feynman diagrams, at one loop in the general case and up to two loops in the fundamental sector. In the pure adjoint sector at one loop we confirm exact agreement with the corresponding amplitudes in $$ \mathcal{N}=4 $$ SYM theory, supporting the idea that a closed subsector of the SCQCD might be exactly integrable. External matter in the fundamental representation breaks dual conformal invariance already at one-loop order while the principle of maximal transcendentality is respected up to two loops.
Highlights
One of the most surprising novelty is that planar MHV scattering amplitudes of N = 4 SYM theory enjoy an additional dynamical symmetry, which is not present in the Lagrangian formulation and which constrains the form of the amplitudes to be much simpler than a naive analysis might suggest [1, 2]
In the dimensional reduction scheme, assigning transcendentality −1 to the dimensional regularization parameter, one obtains L-loop corrections with uniform degree of transcendentality 2L. This maximal transcendentality property was first observed for the anomalous dimension of twist-2 operators [11,12,13] and was found it is surprisingly enjoyed by all the known observables of the theory. It is still unclear whether this property has to be ascribed to the special diagrammatics [14] associated to eitherconformal symmetry or supersymmetry, or if it is a unique feature of the model
The complete set of four-point amplitudes of the theory can be obtained by means of supersymmetry transformations from superamplitudes involving only the chiral scalar superfields Φ and Q as external particles
Summary
The complete set of four-point amplitudes of the theory can be obtained by means of supersymmetry transformations from superamplitudes involving only the chiral scalar superfields Φ and Q as external particles. The other component amplitudes can be obtained by choosing different projections of the superspace results. We draw super Feynman diagrams contributing to the four-point scalar supervertex associated to the chosen external configuration, where the diagrams have to be suitably chosen to respect the color ordering. In order to extract the four-point component amplitude with scalar fields as external particles we perform the projection d4x d4θ · · · = d4x D 2D2 . The contributions of the different diagrams is summed up and the final result is expressed, using the integration by part reduction technique, as a linear combination of master integrals (see [50] for details).
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