1. Mirage Mediation of Supersymmetry Breaking: Phenomenology and Cosmology Masahiro Yamaguchi (Tohoku University) Sep. 25, 2008 @TeVPA, Beijing

2. 2 Talk Plan Introduction and motivation New Theoretical developments in SUSY Mirage Mediation Moduli/Gravitino problem and a solution Summary

3. 3 Call for Particle Physics beyond Standard Model Stabilization of Weak Scale Neutrino Masses and Mixing Components of Universe (dark energy) dark matter baryons (baryogenesis)

4. 4 Low-Energy Supersymmetry Promising candidate for Beyond-Standard-Model Symmetry between bosons and fermions Thanks to difference of statistics, quantum corrections tend to cancel (at least partially).  no quadratic divergence in Higgs mass  stabilizes weak scale due to (broken) symmetry Unification of gauge forces in SUSY Lightest superparticle (LSP) stable (if R-parity conservation), and a natural dark matter candidate

5. 5 Even if SUSY is a correct solution, there are still a wide variety of possibilities. Example: SUSY breaking scale and gravitino mass Gravitino Mass m 3/2 ~ F/M Pl Sparticle Mass m ~F/M (M: messenger scale) M~10 5 GeV—10 20 GeV  m/m 3/2 ~ M/M Pl (m 3/2 >> 100TeV split SUSY?) m 3/2 ~ 100TeV anomaly mediation mirage mediation (this talk) m 3/2 ~ 1 TeV gravity mediation m 3/2 << 1 TeV gauge mediation Phenomenology/Cosmology are different for a different value of gravitino mass.

6. 6 LHC (Large Hadron Collider) Experiment pp collider at CERN Center of mass energy =14 TeV Starts in 2008! Expects new physics discovery at TeV scale New Ideas will be tested at LHC!

7. 7 2. Recent Theoretical Developments in SUSY Meta-Stable SUSY Breaking Vacua simple realization of SUSY breaking Moduli Stabilization in Superstring Theory (KKLT) First realization of stabilization of all moduli/dilaton based on flux compactification + non-perturbative effects (e.g. gaugino condensation) Intriligator, Seiberg, & Shih ‘06 Kachru,Kallosh, Linde&Trivedi ‘03

8. 8 Meta Stable SUSY Breaking Vacua Difficulty of dynamical SUSY breaking chiral gauge theory  Witten index (broken) R-symmetry model building possible, but very non-trivial New possibility SUSY preserving in true vacuum SUSY is broken in meta-stable vacuum (with long life time) This is realized in many generic models such as SUSY QCD with massive flavors. Intriligator, Seiberg, & Shih ‘06

9. 9 Advantages SUSY breaking occurs in rather a generic set-up. Model building becomes easier, in particular, in gauge mediation. No light R-axion  cosmologically safer

10. 10 Moduli Stabilization String Theory moduli fields: size and shape of extra dimensions dilaton field: string coupling constant Moduli stabilization Flat directions at tree level  gauge couplings, masses not fixed  new long range force (  disaster) Some non-trivial effects are needed to stabilize moduli/dilation long standing problem since 80’s

11. 11 New Mechanism: Flux Compactifications Higher rank tensors in string theory e.g. type IIB superstring Superpotential Switch on fluxes  generation of superpotential for shape moduli  stabilizing shape moduli (and dilaton) 2 form field : 3 form field strength : shape (or complex) moduli Giddings-Kachru- Polchinski ‘02

12. 12 KKLT Set-Up Overall moduli (Kaehler moduli) not yet stabilized One needs further steps 1) non-perturbative effects for Kaehler moduli (known effects, e.g. gaugino condensate) –Kaehler moduli stabilized –Anti de-Sitter space with SUSY unbroken 2) Uplifting by some SUSY breaking source (e.g. anti-D brane/ dynamical SUSY breaking)  Minkowski space with SUSY breaking Kachru-Kallosh-Linde-Trivedi 03

13. 13 3. Mirage Mediation

14. 14 Implications to Low-E SUSY Original Motivation of KKLT: realization of dS vacuum in string theory Simple KKLT set-up can also provide a new mediation mechanism of SUSY breaking. Sparticle mass spectrum mixture of moduli and anomaly mediation = mirage mediation Choi-Falkowski-Nilles -Olechowski-Pokorski 04,05 Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05 and subsequent papers

15. 15 Phenomenology with KKLT-type model SUSY breaking sector added to uplift potential SUSY breaking by moduli is sub-dominant Overall SUSY breaking characterized by gravitino mass: little hierarchy among masses: Moduli T gravitino sparticles (compensator  ) F T ~m 3/2 2 /m T << F  = m 3/2 m T >> m 3/2 >> m soft ~10 4 TeV ~100 TeV ~ 1 TeV

16. 16 Gaugino Masses @GUT scale moduli+anomaly mediation: two contributions comparable Consider SM on D7 brane Gauge kinetic function Gaugino Mass

17. 17 Gaugino Masses For R~35 (KKLT), M 1 : M 2 : M 3 ~1 : 1.3: 2 cf. M 1 : M 2 : M 3 ~1: 2: 7 (mSUGRA)

18. 18 Mirage Mediation RG properties: Gaugino masses are unified at a mirage scale. Similar argument to scalar masses Choi, Jeong, Okumura 05 from Lebedev, Nilles, Ratz 05

19. 19 General Features of Mirage Mediation Compressed Sparticle Mass Spectrum small  parameter (~M 1 )  small gluino mass/ RGE LSP(lightest superparticle): neutralino admixture of gauginos and higginos (somewhat model dependent) stau: tends to be light Mass Spectrum is very different from mSUGRA (CMSSM) gauge mediation & anomaly mediation Testable at future collider experiments (LHC/ILC) Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

20. 20 Thermal Relic Neutralino Relic Abundance Detection Rate (SI) Choi-Lee-Shimizu-Kim-Okumura 06

21. 21 4. Potential Problem and Resolution Cosmological Moduli Problem Potential minimum during inflation is in general different from true minimum.  displacement from true minimum Damped coherent oscillation will dominate energy density of the universe Moduli are heavy. lifetime shorter than 1 sec. no entropy crisis But …….

22. 22 Life is not so easy! Moduli-induced Gravitino Problem Moduli decay into gravitino pair with Br.~0.01 Dangerous decay chain: moduli  gravitini  sparticles  LSPs Overabundance of LSPs Gravitino mass must be heavier than ~10 6 GeV to escape overclosure constraint. (wino case) Even severer constraint on gravitino mass for other neutralino case Endo,Hamaguchi,Takahashi 06 Nakamura,MY 06 cf. Joichi-MY ‘95

23. 23 Resolutions Modifications of moduli potential no shift of minimum during inflation e.g. symmetry enhancement Concrete realization of this idea?? Lighter LPSs Nakamura-Okumura-MY ‘08 Model with axino LSP solves the LSP-overabundance problem and also mu/B problem in SUSY

24. 24 Cosmology Highlight axino dark matter Axino can be dark matter when mass ~0.1 GeV. Axinos are produced energitically.  Free-streaming length O(0.1) MPc. Maybe some implication to (small) scale structure axino abundance for typical NLSP

25. 25 Phenomenology Highlights  Neutralino NLSP decay (to Axino) decay length bino-like NLSP: very long higgsino-like NLSP  displaced vertex to h/Z: specutacular signals at LHC!  Sparticle Mass Spectrum general mixture of Moduli/Gauge/Anomaly mediation Mirage unification still holds for gaugino masses. This is not the case for scalar masses. Everret et al ‘08 Choi et al, in preparation Nakamura,Okumura,MY 08, and work in progress

26. 26Summary Low-Energy SUSY: promising candidate for beyond SM  discovery at LHC ? SUSY Pheno/Cosmology: sensitive to mediation mechanism of SUSY breaking New Developments meta-stable SUSY breaking vacua  gauge mediation moduli stabilization a la KKLT  mirage mediation Models of mirage mediation considered Sparticle Masses (anomaly+moduli mediation) Thermal Relic Neutralinos can be DM Potential moduli/gravitino problem  axino DM?