Natural Solution to the Supersymmetry Electroweak Fine-Tuning Problem

Tianjun Li

Institute of Theoretical Physics, Chinese Academy of Sciences

Yellow Mountain, May 9, 2014

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

I. Introduction

Gauge Hierarchy Problem

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Gauge Coupling Unification

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BICEP2

• The inflation scale is the GUT scale.

• The inflaton potential: non-renormalized theorem for superpotential.

• M^2_{EW} \sim M_{\nu} H

II. SUSY EW Fine-Tuning Problem

• Higgs Boson Mass

• LHC SUSY Search

• Fine-Tuning Problem

• 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

%01.0~/~/ 2222~ ZZH mmmmtu

•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

222~6)tan/(t

mAX tt •Stop maximal/large mixing can improves it by about two orders

•The Lightest CP-Even Higgs Boson Mass

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.

mSUGRA/CMSSM

•Gluino 1.4TeV

•Squark 1.8TeV

•https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots#SusyGttSummary

Simplified model: MET+jets

•ATLAS-CONF-2013-047

•Gluino 1.8TeV

•Squark 1.8TeV

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Supersymmetric SMs

• Displaced Supersymmetry

• Double Invisible Supersymmetry

III. The MSSM with Heavy LSP

Phenomenological Constraints

• The anomalous magetic momentum of the muon

• Higgs boson mass

• LHCb

Parameter Scan

IV. No-Scale F-SU(5)

Flipped SU(5) Model

No-Scale Supergravity

Supergravity Potential:

Natural Solution to EW SUSY Fine-Tuning

Natural Solution to EW SUSY Fine-Tuning

No-Scale F-SU(5)

• \mu problem: Giudice-Masiero (GM) mechanism

• All the mass parameters are proportional to

Natural Solution to the EWFT problem:

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.

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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