Renormalization in General Gauge Mediation

TL;DR

This paper explores the renormalization of General Gauge Mediation (GGM) using the current superfield approach, linking supersymmetry breaking to axial vector symmetry breakdown in a sigma model, and deriving gaugino and sfermion masses.

Contribution

It introduces a method to derive and renormalize current superfields in GGM, connecting supersymmetry breaking to sigma model symmetries, and expresses MSSM masses via wavefunction renormalization.

Findings

Derived the current superfield from the supersymmetric linear sigma model.

Computed 2-point functions and performed renormalization using dimensional regularization.

Expressed MSSM gaugino and sfermion masses in terms of wavefunction renormalization constants.

Abstract

We revisit General Gauge Mediation (GGM) in light of the supersymmetric (linear) sigma model by utilizing the current superfield. The current superfield in the GGM is identified with supersymmetric extension of the vector symmetry current of the sigma model while spontaneous breakdown of supersymmetry in the GGM corresponds to soft breakdown of the axial vector symmetry of the sigma model. We first derive the current superfield from the supersymmetric linear sigma model and then compute 2-point functions of the current superfield using the (anti-)commutation relations of the messenger component fields. After the global symmetry are weakly gauged, the 2-point functions of the current superfield are identified with a part of the 2-point functions of the associated vector superfield. We renormalize them by dimensional regularization and show that physical gaugino and sfermion masses of the MSSM are expressed in terms of the wavefunction renormalization constants of the component fields of the vector superfield.