The one-loop effective potential of the Wess-Zumino model revisited

TL;DR

This paper recalculates the one-loop effective potential of the Wess-Zumino model using superfield techniques, deriving the auxiliary field potential for the first time and addressing previous contradictory results.

Contribution

It provides a comprehensive calculation of the one-loop effective potential, including the auxiliary field potential, using superfield methods for the first time.

Findings

The Kähler potential matches previous results from 1993.

The auxiliary field potential is derived for the first time.

Discussion of convergence issues in the calculations.

Abstract

The full one-loop supersymmetric effective potential for the Wess-Zumino model is calculated using superfield techniques. This includes the K\"ahler potential and the auxiliary field potential, of which the former was originally computed in 1993 while the latter is derived for the first time. In the purely bosonic sector our results match those of older component field calculations. In light of prior contradictory results found in the literature, the calculation of the leading term in the auxiliary field potential is approached in a variety of ways. Issues related to conditional convergence that occur during these calculations and their possible consequences are discussed.