The Super-Natural Supersymmetry and Its Classic Example: M-Theory Inspired NMSSM

Abstract

We briefly review the super-natural supersymmetry (SUSY), which provides a most promising solution to the SUSY electroweak fine-tuning problem. In particular, we address its subtle issues as well. Unlike the Minimal Supersymmetric Standard model (MSSM), the Next to MSSM (NMSSM) can be scale invariant and has no mass parameter in its Lagrangian before SUSY and gauge symmetry breakings. Therefore, the NMSSM is a perfect framework for super-natural SUSY. To give the SUSY breaking soft mass to the singlet, we consider the moduli and dilaton dominant SUSY breaking scenarios in M-theory on $S^1/Z_2$. In these scenarios, SUSY is broken by one and only one $F$-term of moduli or dilaton, and the SUSY breaking soft terms can be determined via the Kähler potential and superpotential from Calabi-Yau compactification of M-theory on $S^1/Z_2$. Thus, as predicted by super-natural SUSY, the SUSY electroweak fine-tuning measure is of unity order. In the moduli dominant SUSY breaking scenario, the right-handed sleptons are relatively light around 1 TeV, stau can be even as light as 580 GeV and degenerate with the lightest neutralino, chargino masses are larger than 1 TeV, the light stop masses are around 2 TeV or larger, the first two-generation squark masses are about 3 TeV or larger, and gluinos are heavier than squarks. In the dilaton dominant SUSY breaking scenario, the qualitative picture remain the same but we have heavier spectra as compared to moduli dominant SUSY breaking scenario. In addition to it, we have Higgs $H_2/A_1$-resonance solutions for dark matter (DM). In both scenarios, the minimal value of DM relic density is about 0.2. To obtain the observed DM relic density, we can consider the dilution effect from supercritical string cosmology or introduce the axino as the lightest supersymmetric particle.

35 pages, 12 figures and two tables

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• Current Status of Natural NMSSM in Light of LHC 13TeV Data and XENON-1T Results
• Constraining Natural SUSY via the Higgs Coupling and the Muon Anomalous Magnetic Moment Measurements
• Higgs Mass and Muon $g-2$ Anomaly in MSSM with Gauge-Gravity hybrid Mediation
• New Physics Search at the CEPC: a General Perspective
• Quasi Yukawa Unification and Fine-Tuning in U(1) Extended SSM
• No-Scale $\mu$-Term Hybrid Inflation
• $B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-}$ and its impact on $B_{s,d}\to {\mu }^{+}{\mu }^{-}$
• Status of Natural Supersymmetry from the GmSUGRA in Light of the current LHC Run-2 and LUX data
• Low Fine Tuning in Yukawa-deflected Gauge Mediation
• The PeV-Scale Split Supersymmetry from Higgs Mass and Electroweak Vacuum Stability
• Probing the Supersymmetric Grand Unified Theories at the Future Proton-Proton Colliders and Hyper-Kamiokande Experiment
• The Right-Handed Slepton Bulk Region for Dark Matter in Generalized No-scale $\mathcal{F}$-$SU(5)$ with Effective Super-Natural Supersymmetry