Supergraph Approach in a Higher-order LDE Calculation of the Effective Potential for F-type Broken SUSY

TL;DR

This paper develops a supergraph approach combined with the linear delta expansion to compute the effective potential in a supersymmetry-breaking model, demonstrating the method's effectiveness and potential for broader applications in supersymmetric theories.

Contribution

It introduces a supergraph method integrated with LDE for calculating the effective potential in broken SUSY models, enabling semi-nonperturbative superspace computations.

Findings

Supergraph approach successfully applied to SUSY-breaking models.

LDE method effective up to order δ² in superspace calculations.

Potential for extending to MSSM precision tests.

Abstract

In this work, we adopt the simplest model that spontaneously breaks supersymmetry, namely, the minimal O'Raifeartaigh model. The effective potential is computed in the framework of the linear delta expansion (LDE) approach up to the order $\delta^2$, conjugated with superspace and supergraph techniques. The latter can be duly mastered even if supersymmetry is no longer exact and the efficacy of the superfield approach in connection with the LDE procedure is confirmed according to our investigation. That opens up a way for a semi-nonperturbative superspace computation which allows us to deal with spontaneously broken supersymmetric models and encourages us to go further and apply this treatment to the Minimal Supersymmetric Standard Model (MSSM) precision tests.