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 finetuning. Depending on the high-scale model and fine-tuning definition, we find a minimal fine-tuning of 3 − 38 (corresponding to O(10 − 1)%) for the low-scale measure, and 63 − 571 (corresponding to O(1 − 0.1)%) for the high-scale measure. In addition, minimally finetuned spectra give rise to a dark matter relic density that is between 10 −3 < Ωh 2 < 1, when µ 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.

Dark matter, fine-tuning and (g-2)_{\mu} in the pMSSM

“…The degree of FT in constrained models that explain the (g −2) µ discrepancy is studied in [60,61], whereas the role of FT in spectra with the right DM properties is studied in Ref. [62][63][64][65][66].…”

The hierarchy problem of the Standard Model and its solutions

“…The measure ∆ defined above for the FT is known as Barbieri-Giudici measure [30]. Though model dependent [31], Eq. (1.16) may be applied to any theory and it represents very well the conceptual idea of FT.…”

“…It can, however, have non-perturbative effects [1,21,88]. For instance, in a free theory with a massless Dirac fermion ψ charged under this gauge group, the Lagrangian is invariant under the transformations of the following global group, 31) where U (1) V transforms left-and right-handed fermions in the same way, while U (1) A transforms them with opposite phases. For this reason they are called vector and axial symmetries, respectively.…”

“…31) where U = U[Π ]. AsΦ contains no information on the NGB, it can only transform under elements of H, henceΦ…”

Aspects of fine-tuning in theories with extended scalar sectors

“…Furthermore, there will be effects from the RG running from the UV scale to approximately the TeV scale. Although the exact results are very model dependent, it has been shown [51] that this can greatly restrict the applicability of high-energy SUSY models as natural extensions of the SM.…”