Approximate Analytic Solutions of RG Equations for Yukawa and Soft Couplings in SUSY Models

TL;DR

This paper derives simple analytical formulas for solving RG equations in SUSY models, accurately capturing Yukawa and soft couplings' behavior, including fixed points, with validation against numerical solutions.

Contribution

It provides new analytical solutions for RG equations in SUSY models, including soft couplings, with explicit fixed point analysis and comparison to numerical results.

Findings

Analytical solutions match numerical results within a few percent.

Solutions exhibit fixed point behavior analytically.

Formulas apply to Yukawa and soft couplings in SUSY theories.

Abstract

We present simple analytical formulae which describe solutions of the RG equations for Yukawa couplings in SUSY gauge theories with the accuracy of a few per cent. Performing the Grassmannian expansion in these solutions one finds those for all the soft couplings and masses. The solutions clearly exhibit the fixed point behaviour which can be calculated analytically. A comparison with numerical solutions is demonstrated.