Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Minima

TL;DR

This work delivers a comprehensive analytic treatment of dangerous directions in the MSSM scalar potential, rigorously classifying and constraining both unbounded-from-below (UFB) and charge-and-color-breaking (CCB) directions. By incorporating proper one-loop corrections through scale-optimized minimization and deriving necessary-and-sufficient analytic bounds, the authors show that large regions of MSSM parameter space are excluded not only by A-terms but also by B- and M-parameters, with UFB-3 typically providing the strongest restriction. The analysis spans all couplings, uses universal soft terms at the high scale, and translates the constraints into explicit, scalable inequalities evaluated at carefully chosen $\hat Q$ scales. The results markedly bolster the MSSM’s predictive power, guiding model-building and highlighting regions where metastability or alternative SUSY-breaking schemes may be required.

Abstract

A complete analysis of all the potentially dangerous directions in the field-space of the minimal supersymmetric standard model is carried out. They are of two types, the ones associated with the existence of charge and color breaking minima in the potential deeper than the realistic minimum and the directions in the field-space along which the potential becomes unbounded from below. The corresponding new constraints on the parameter space are given in an analytic form, representing a set of necessary and sufficient conditions to avoid dangerous directions. They are very strong and, in fact, there are extensive regions in the parameter space that become forbidden. This produces important bounds, not only on the value of $A$, but also on the values of $B$ and $M_{1/2}$. Finally, the crucial issue of the one-loop corrections to the scalar potential has been taken into account in a proper way.