SUSY Jumps Out of Superspace in the Supersymmetric Standard Model

The supersymmetric standard model (SSM) appears to be firmly grounded in superspace. For example, it would be natural to assume that all the physically important composite operators can be made by combining superfields and superspace derivatives. But even for the simplest possible, free, massless and unbroken SUSY theory in 3+1 dimensions, this is not true. This paper shows that there is a large set of physically important composite operators in the SSM that require explicit factors of the Grassmann odd $\theta$' parameters of superspace. These explicitly break superspace invariance. These composite operators will be called Outfields’, because they are intrinsically `outside’ of superspace. It is not possible to write the Outfields using only superfields and superspace derivatives. The Outfields can be found in the BRST cohomology space of the theory. The calculation of the BRST cohomology space for these theories is performed in this paper using a spectral sequence analysis, starting with the free massless theory, and then adding interactions, and then masses.