The current status of fine-tuning in supersymmetry

Abstract

In this paper, we minimize and compare two different fine-tuning measures in four high-scale supersymmetric models that are embedded in the MSSM. In addition, we determine the impact of current and future dark matter direct detection and collider experiments on the fine-tuning. We then compare the low-scale electroweak measure with the high-scale Barbieri-Giudice measure, which generally do not agree. However, we find that they do reduce to the same value when the higgsino parameter drives the degree of fine-tuning. Depending on the high-scale model and fine-tuning definition, we find a minimal fine-tuning of $3-38$ (corresponding to $\mathcal{O}(10-1)\%$) for the low-scale measure, and $63-571$ (corresponding to $\mathcal{O}(1-0.1)\%$) for the high-scale measure. In addition, minimally fine-tuned spectra give rise to a dark matter relic density that is between $10^{-3} < \Omega h^2 < 1$, when $\mu$ determines the minimum of the fine-tuning. We stress that it is too early to conclude on the fate of supersymmetry, based only on the fine-tuning paradigm.