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 4

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7. Gauge Coupling Unification 7

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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. Stops: Enhancing Higgs mass 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 Tree-level upper bound: Z-boson mass m Z = 91.7 GeV In the MSSM, Higgs quatic coupling at tree-level is determined by EW gauge couplings Stop maximal/large mixing can improves it by about two orders The Lightest CP-Even Higgs Boson Mass

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

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

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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:

51. Natural Solution to EW SUSY Fine-Tuning

53. No-Scale F-SU(5) \mu problem: Giudice-Masiero (GM) mechanism All the mass parameters are proportional to Natural Solution to the EWFT problem:

59. V. General Natural Solution Only one chiral superfield or modulus breaks supersymmetry. All the supersymmetry breaking soft terms are proportional to gravitino mass. \mu term is generated via the GM mechanism after supersymmetry breaking in the MSSM or NMSSM. No-scale supergravity or M-theory on S^1/Z_2.

61. VI. Summary The MSSM with Heavy LSP If all the mass parameters arise from gravitino mass, the fine-tuning will be order one.

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