# Improved predictions for intermediate and heavy Supersymmetry in the MSSM and beyond

## TL;DR

This paper introduces a two-scale matching approach for the MSSM that improves predictions of the SUSY mass spectrum and Higgs mass at high SUSY scales, reducing uncertainties in the model's predictions.

## Contribution

It presents a novel two-scale matching method for the MSSM, enhancing the accuracy of spectrum and Higgs mass predictions at large SUSY scales, and integrates this into SPheno and SARAH tools.

## Key findings

- Improved Higgs mass prediction for large SUSY masses.
- Enhanced gauge coupling unification analysis.
- Extended spectrum generator capabilities.

## Abstract

For a long time, the minimal supersymmetric standard model (MSSM) with light masses for the supersymmetric states was considered as the most natural extension of the Standard Model of particle physics. Consequently, a valid approximation was to match the MSSM to the precision measurement directly at the electroweak scale. This approach was also utilized by all dedicated spectrum generators for the MSSM. However, the higher the supersymmetric (SUSY) scale is, the bigger the uncertainties which are introduced by this matching. We point out important consequences of a two-scale matching, where the running parameters within the SM are calculated at $M_Z$ and evaluated up to the SUSY scale, where they are matched to the full model. We show the impact on gauge coupling unification as well as the SUSY mass spectrum. Also the Higgs mass prediction for large supersymmetric masses has been improved by performing the calculation within an effective SM. The approach presented here is now also available in the spectrum generator SPheno. Moreover, also SARAH was extended accordingly and gives the possibility to study these effects now in many different supersymmetric models.