Parameter Bounds in the Supersymmetric Standard Model from Charge/Color Breaking Vacua

TL;DR

This paper determines bounds on the trilinear coupling in the MSSM by analyzing charge and color breaking vacua, providing numerical limits that refine previous analytical estimates.

Contribution

It introduces a numerical method to calculate more accurate charge/color breaking bounds in the MSSM, improving upon existing analytical limits.

Findings

Numerical bounds are more restrictive than analytical estimates.

Charge/color breaking limits depend on the detailed potential minimization.

Results are presented as best-fit surfaces for the parameter space.

Abstract

We calculate limits on the trilinear soft-breaking parameter, $A_{t}$, in the Minimal Supersymmetric Standard model by requiring the absence of nonzero top squark vacuum expectation values. Assuming a low $\tan\beta$, which implies a large top Yukawa coupling, we also calculate one-loop corrections to the effective potential. The resulting numerical calculations of the charge/color breaking limits are presented as best-fit surfaces. We compare these results with the analytical limit, $A_{t}^{2} < 3(m_{2}^{2}+m_{q}^{2}+m_{t}^{2})$, and find that although this bound is a good estimate of the charge/color breaking bounds for a simplified model of the top sector, stricter bounds are found by a numerical minimization of the Minimal Supersymmetric Standard Model potential.