SUSY Jumps Out of Superspace in the Supersymmetric Standard Model

TL;DR

This paper reveals that in the supersymmetric standard model, many important composite operators, called Outfields, inherently break superspace invariance and cannot be constructed solely from superfields and derivatives, challenging traditional superspace assumptions.

Contribution

It demonstrates the existence of Outfields that require explicit Grassmann parameters, and computes their BRST cohomology using spectral sequence analysis in the SSM.

Findings

Outfields require explicit Grassmann parameters, breaking superspace invariance.

BRST cohomology analysis identifies and characterizes Outfields.

Outfields are essential for understanding composite operators in the SSM.

Abstract

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.