Superconformally Covariant OPE and General Gauge Mediation

TL;DR

This paper uses broken superconformal symmetry and the super OPE to analyze hidden sectors in gauge mediation, relating UV properties to IR effects and providing a method to approximate visible sector soft masses.

Contribution

It introduces a framework applying superconformal symmetry and the super OPE to constrain hidden sector theories in gauge mediation, even when broken.

Findings

Relates OPE coefficients of superconformal descendants to primaries.

Connects correlator discontinuities to scattering cross sections.

Proposes truncating the OPE for practical soft mass calculations.

Abstract

We consider using broken superconformal symmetry and the super operator product expansion (sOPE) to constrain and analyze hidden sector theories that couple to our gauge forces and are not necessarily weakly coupled. Conformal and supersymmetry breaking are IR effects, associated with field or spurion expectation values, whereas the sOPE is determined in the UV and hence does not notice the breaking. The broken superconformal symmetry relates OPE coefficients of superconformal descendant operators to those of the superconformal primaries. We apply these ideas to the current correlators of general gauge mediation (GGM). We also consider analyticity properties of these correlators, e.g. their discontinuities, and use the optical theorem to relate them to total scattering cross sections from visible to hidden sector states, e.g. sigma(vis + vis --> hidden), analogous to sigma(e+ e- --> hadrons) in QCD. We discuss how the current-current OPE can be truncated to the first few terms to get a good approximation to the visible sector soft masses of GGM.