Natural Solution to the Supersymmetry Electroweak Fine-Tuning Problem

1. Natural Solution to the Supersymmetry Electroweak Fine-Tuning Problem Tianjun Li Institute of Theoretical Physics, Chinese Academy of Sciences Yellow Mountain, May 9, 2014

2. Outline • I. Introduction • II. The SUSY EW Fine-Tuning Problem • III. The MSSM with the Heavy LSP • IV. No-Scale F-SU(5) • V. General Natural Solution • VI. Summary

3. I. Introduction

4. Gauge Hierarchy Problem

7. Gauge Coupling Unification

13. BICEP2 • The inflation scale is the GUT scale. • The inflaton potential: non-renormalized theorem for superpotential. • M^2_{EW} \sim M_{\nu} H

14. II. SUSY EW Fine-Tuning Problem • Higgs Boson Mass • LHC SUSY Search • Fine-Tuning Problem

15. The Lightest CP-Even Higgs Boson Mass • Stops: Enhancing Higgs mass • Tree-level upper bound: Z-boson mass mZ = 91.7 GeV • In the MSSM, Higgs quatic coupling at tree-level • is determined by EW gauge couplings • Correct the quartic coupling and enhance Higgs boson mass • Stop maximal mixing relaxing the little hierachy problem • Without large stop mixing, we need • 10 TeV stops, rendering a fine-tuning • Stop maximal/large mixing can improves it by about two orders

16. LHC SUSY Search • Gluino and squark masses around 1.7 TeV in the CMSSM and mSUGRA. • Gluino mass low bound is around 1.3 TeV. • Stop/sbottom mass low bounds are around 600 GeV. • If the LSP is heavy, all the bounds can be relaxed.

20. mSUGRA/CMSSM • Squark 1.8TeV • Gluino 1.4TeV • https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots#SusyGttSummary

21. Simplified model: MET+jets • Squark 1.8TeV • Gluino 1.8TeV • ATLAS-CONF-2013-047

31. Supersymmetric SMs • Displaced Supersymmetry • Double Invisible Supersymmetry

32. III. The MSSM with Heavy LSP

34. Phenomenological Constraints • The anomalous magetic momentum of the muon • Higgs boson mass • LHCb

35. Parameter Scan

39. IV. No-Scale F-SU(5)

41. Flipped SU(5) Model

50. No-Scale Supergravity Supergravity Potential: