# Quadratic Contributions of Softly Broken Supersymmetry in the Light of Loop Regularization

## TL;DR

This paper uses loop regularization to demonstrate that softly broken supersymmetric theories, specifically the Wess-Zumino model, do not exhibit quadratic divergences up to two loops, confirming supersymmetry's protective features.

## Contribution

It explicitly shows, through Feynman diagram calculations, that quadratic divergences cancel in softly broken supersymmetric models using loop regularization.

## Key findings

- Quadratic divergences cancel up to two loops in the Wess-Zumino model.
- Loop regularization respects supersymmetry and gauge symmetry.
- Results align with supergraph techniques.

## Abstract

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To demonstrate further its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques.