Effective K\"ahler and auxiliary field potentials for chiral superfield models at three loops

TL;DR

This paper calculates the three-loop effective K"ahler potential for general supersymmetric chiral models and extends the auxiliary field potential results for the Wess-Zumino model, revealing a surprisingly simple structure.

Contribution

It provides the first three-loop effective K"ahler potential for general chiral superfield theories and extends auxiliary field potential results for the Wess-Zumino model.

Findings

Three-loop effective K"ahler potential involves only four terms.

Simplified structure with three distinct renormalized master integrals.

Extended auxiliary field potential results to three-loop order for Wess-Zumino model.

Abstract

I obtain the effective K\"ahler potential at three-loop order for a general renormalizable supersymmetric theory containing only chiral supermultiplets. The three-loop contribution is remarkably simple, consisting of only four terms involving three distinct renormalized master integrals. In the case of the Wess-Zumino model with a single chiral superfield, I also obtain the effective auxiliary field potential at three-loop order, extending previous results at one-loop order. The method used is inferential, relying on existing knowledge of the ordinary scalar effective potential.