$ \mathcal{N}= 1 $ super Feynman rules for any superspin: Noncanonical SUSY

Abstract

Super Feynman rules for any superspin are given for massive $ \mathcal{N}=1 $ supersymmetric theories, including momentum superspace on-shell legs. This is done by extending, from space to superspace, Weinberg's perturbative approach to quantum field theory. Superfields work just as a device that allow one to write super Poincare-covariant superamplitudes for interacting theories, relying neither in path integral nor canonical formulations. Explicit transformation laws for particle states under finite supersymmetric transformations are offered. $ \mathit{C}, \mathit{P}, \mathit{T}, $ and $ \mathcal{R} $ transformations are also worked out. A key feature of this formalism is that it does not require the introduction of auxiliary fields, and when introduced, their purpose is just to render supersymmetric invariant the time-ordered products in the Dyson series. The formalism is tested for the cubic scalar superpotential. It is found that when a superparticle is its own antisuperparticle the lowest-order correction of time-ordered products, together with its covariant part, corresponds to the Wess-Zumino model potential.