$\theta$-diagram technique for $\mathcal{N}=1$, $d=4$ superfields

TL;DR

This paper introduces a new diagrammatic method for Grassmann integration in 4d $ ext{N}=1$ superfield theories, providing an algorithmic approach that simplifies calculations compared to traditional $D$-algebra methods.

Contribution

We develop a novel, algorithmic diagrammatic technique for Grassmann integration in super-Feynman diagrams, implemented as a Mathematica program for efficient computation.

Findings

The method is applicable to vector, chiral, and anti-chiral superfields.

It simplifies Grassmann integrations into polynomial expressions in momenta.

The approach is demonstrated with theories similar to $ ext{N}=2$ SYM with massless matter.

Abstract

We describe a diagrammatic procedure to carry out the Grassmann integration in super-Feynman diagrams of 4d theories expressed in terms of $\mathcal{N}=1$ superfields. This method is alternative to the well known $D$-algebra approach. We develop it in detail for theories containing vector, chiral and anti-chiral superfields, with the type of interactions which occur in $\mathcal{N}=2$ SYM theories with massless matter, but it would be possible to extend it to other cases. The main advantage is that this method is algorithmic; we implemented it as a Mathematica program that, given the description of a super Feynman diagram in momentum space, returns directly the polynomial in the momenta produced by the Grassmann integration.