We identify the parameter regions of the phenomenological minimal supersymmetric standard model (pMSSM) with the minimal possible fine-tuning. We show that the fine-tuning of the pMSSM is not large, nor under pressure by LHC searches. Low sbottom, stop and gluino masses turn out to be less relevant for low fine-tuning than commonly assumed. We show a link between low fine-tuning and the dark matter relic density. Fine-tuning arguments point to models with a dark matter candidate yielding the correct dark matter relic density: a bino-higgsino particle with a mass of 35 − 155 GeV. Some of these candidates are compatible with recent hints seen in astrophysics experiments such as Fermi-LAT and AMS-02. We argue that upcoming direct search experiments, such as XENON1T, will test all of the most natural solutions in the next few years due to the sensitivity of these experiments on the spin-dependent WIMP-nucleon cross section.It is expected that the Standard Model of particle physics (SM) is only an effective theory that needs to be complemented at higher energies. The problem of extending the SM arises in the high sensitivity of the Higgs potential to the mass scale of new physics. If this scale largely exceeds the electroweak scale we generally have the socalled fine-tuning (FT) problem: a huge degree of cancellation is needed between the tree-level mass and the independent quantum corrections to match the measured Higgs boson mass [1]. For many years supersymmetry (SUSY) [2] with particles at the TeV scale was regarded to be the most natural solution to the FT problem due to a cancellation of fermionic and bosonic contributions to the quantum corrections [3,4]. Furthermore, SUSY is motivated as providing the most general space-time symmetry, a unification of coupling constants and a starting point to solve the shortcomings of the SM. In addition, R-parity conserving SUSY provides through the lightest neutralino (χ 0 1 ) one of the best weakly interacting massive particle (WIMP) candidates for dark matter (DM). Within the ΛCDM model, Planck measurements of the cosmic microwave background yield a value for the dark matter relic density: Ω DM,Planck h 2 = 0.1186 ± 0.0011 [5]. Due to the null results at the various collider and DM experiments, there is a growing current of opinion that SUSY is just another beautiful idea that didn't pan out. The main argument is that SUSY particles already need to be so heavy, that SUSY itself requires a significant amount of FT to reproduce the electroweak scale correctly, making the theory unnatural independent of the FT measure used [6][7][8]. One must realize that this statement is framework dependent, e.g. particular GUT scale models such as CMSSM or gauge-mediated SUSY are indeed fine-tuned [9][10][11][12] . However, this is no longer true if we consider a less constrained SUSY extension of the SM [13][14][15][16][17]. In this paper we re-evaluate the FT of SUSY by looking at the minimal SUSY extension of the SM (MSSM), restricted to the phenomenologically most relevant soft SUSY ...

In the literature measures of fine-tuning have been discussed as one of the tools to assess the feasibility of beyond the Standard Model theories. In this paper we focus on two specific measures and investigate what kind of fine-tuning they actually quantify. First we apply both measures to the two Higgs doublet model, for which one can analyze the numerical results in terms of available analytic expressions. After drawing various conclusions about the finetuning measures, we investigate a particular left-right symmetric model for which it has been claimed that already at tree-level it suffers from a high amount of fine-tuning. We will reach a different conclusion, although left-right symmetric models may require a modest amount of fine-tuning if phenomenological constraints are imposed. Our analysis shows that the two considered measures can probe different aspects of fine-tuning and are both useful if applied and interpreted in the appropriate way. * d.boer@rug.nl

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