# A new approach to gauge coupling unification and proton decay

## TL;DR

This paper introduces an analytical method incorporating two-loop RG running to connect supersymmetric and GUT spectra, enabling detailed exploration of proton decay predictions across various GUT models.

## Contribution

It develops a formalism to analyze the interplay between SUSY breaking patterns and proton lifetime predictions in different GUT models.

## Key findings

- Constraints on SUSY spectra from proton lifetime limits
- Predictions for proton decay in specific GUT models
- Insights into SUSY breaking patterns compatible with experimental bounds

## Abstract

An analytical formalism, including RG running at two loop order, is used to link the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between the pattern of supersymmetry breaking and the prediction for the proton lifetime. With this formalism at hand, we study three concrete GUT models: (i) Minimal SU(5) SUSY GUT, (ii) Missing Partner SU(5) SUSY GUT, and (iii) an orbifold SU(5) SUSY GUT. In each case we derive interesting conclusions about the possible patterns of the supersymmetric spectrum once the present limits on the proton lifetime are imposed, and vice versa, we obtain the predictions for the proton lifetime for specific viable choices of the SUSY spectrum.