Supersymmetry with dark matter is still natural

Melissa van Beekveld, Wim Beenakker, Sascha Caron, Ruud Peeters, and Roberto Ruiz de Austri

Phys. Rev. D 96, 035015 – Published 17 August 2017

Abstract

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.

Received 23 January 2017

DOI:https://doi.org/10.1103/PhysRevD.96.035015

Physics Subject Headings (PhySH)

Hierarchy problem Particle dark matter Supersymmetric models Weakly interacting massive particles

Supersymmetry

Particles & FieldsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Melissa van Beekveld^1,*, Wim Beenakker^1,2,†, Sascha Caron^1,3,‡, Ruud Peeters^4,§, and Roberto Ruiz de Austri^5,∥

¹Institute for Mathematics, Astrophysics and Particle Physics, Faculty of Science, Mailbox 79, Radboud University Nijmegen, P.O. Box 9010, NL-6500 GL Nijmegen, Netherlands
²Institute of Physics, University of Amsterdam, Science Park 904, 1018 XE Amsterdam, Netherlands
³Nikhef, Science Park 110, 1098 XG Amsterdam, Netherlands
⁴Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, Netherlands
⁵Instituto de Física Corpuscular, IFIC-UV/CSIC, C/Catedrático José Beltrán, E-46980 Paterna, Valencia, Spain

^*mcbeekveld@gmail.com
^†w.beenakker@science.ru.nl
^‡scaron@cern.ch
^§r.j.c.peeters@rug.nl
^∥rruiz@ific.uv.es

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Vol. 96, Iss. 3 — 1 August 2017

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Images

Figure 1
Fine-tuning as function of the DM relic density ( $Ω_{DM} h^{2}$ ). Dark brown, maroon and red points indicate that the models are excluded due to mass limits on charged particles at LEP, bounds on the decay widths of the $Z$ - and Higgs bosons, and LUX/PICO measurements on the WIMP-nucleus scattering cross section, respectively. The points indicated in purple are under pressure due to the LHC experiments that look for colored sparticles. In blue we show the allowed model points, with the corresponding DM composition indicated by the hatching. The lila solid curve indicates the predicted sensitivity from XENON1T [60] and the pink dashed curve indicates the predicted sensitivity from a proposed LHC search for bino-higgsino electroweakinos [61]. The yellow band indicates $0.106 < Ω_{DM} h^{2} < 0.130$ .
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Figure 2
The present-day velocity-weighted dark matter annihilation cross section $⟨ σ v ⟩$ ( ${cm}^{3} s^{- 1}$ ) as function of the dark matter mass $m_{DM}$ (GeV) for models with $FT < 10$ (colored) and $FT \geq 10$ (gray) and a relic density between $0.106 < Ω_{DM} h^{2} < 0.130$ . The color code indicates the dominant dark matter annihilation channel: dark blue for $W^{+} W^{-}$ , light blue for $τ^{+} τ^{-}$ , red for $b \bar{b}$ and brown for $q \bar{q}$ . Purple and pink shadings indicate the favored regions to explain the AMS-02 antiproton excess and the Galactic center photon excess. The dark gray line indicates the limit on the DM annihilation cross section derived from observations of dwarf galaxies assuming a 100% annihilation to $b \bar{b}$ [62].
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Figure 3
Lightest chargino, stau, gluino and stop mass versus the DM mass for lowest-FT natural models satisfying all constraints (including the dark matter relic density). The FT is shown in color scale. The ATLAS 13 TeV search limits, produced using simplified SUSY models, are also shown for comparison. However, as explained in the text, these limits actually are not applicable to the majority of our models [74, 75, 76, 77].
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Figure 4
Characteristic mass spectrum for two of our low fine-tuning solutions with the correct relic density. All decays with a branching ratio larger than 10% are indicated by arrows. The decay arrows are plotted with a thickness and color related to the branching ratio (darker represents a higher branching ratio). The figure has been made using PySLHA [78].
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Figure 5
The spin-independent (left) and spin-dependent (right) WIMP-proton cross section versus the dark matter mass for the lowest-FT natural models satisfying all constraints (including the dark matter relic density). The FT is shown in color scale. The $σ_{SI, p}$ XENON1T limit [79] and the $σ_{SD, p}$ PICO-60 limit [54] are also shown for comparison. Note that these experiments assume that the neutron-WIMP and proton-WIMP cross sections are equal to derive these limits. In our models, $σ_{SD, n}$ is always lower than $σ_{SD, p}$ . To illustrate the effect of this, we show in the $σ_{SD, p}$ plot also the $3 σ$ PICO limit for the assumption that $σ_{SD, n} / σ_{SD, p} = 2 / 3$ .
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