Mirage Mediation of Supersymmetry Breaking: Phenomenology and Cosmology

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

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

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. 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. Even if SUSY is a correct solution, there are still a wide variety of possibilities. Example: SUSY breaking scale and gravitino mass Gravitino Mass m3/2 ~ F/MPl Sparticle Mass m ~F/M (M: messenger scale) M~105 GeV—1020 GeV  m/m3/2 ~ M/MPl (m3/2 >> 100TeV split SUSY?) m3/2 ~ 100TeV anomaly mediation mirage mediation (this talk) m3/2 ~ 1 TeV gravity mediation m3/2 << 1 TeV gauge mediation Phenomenology/Cosmology are different for a different value of gravitino mass.

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. 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. Meta Stable SUSY Breaking Vacua Intriligator, Seiberg, & Shih ‘06 • 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.

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. 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. New Mechanism: Flux Compactifications Giddings-Kachru- Polchinski ‘02 • 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

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. 3. Mirage Mediation

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. 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) • FT~m3/22/mT << FF= m3/2 • mT >> m3/2 >> msoft ~104 TeV ~100 TeV ~ 1 TeV

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

17. Gaugino Masses For R~35 (KKLT), M1: M2: M3~1 : 1.3: 2 cf. M1: M2: M3~1: 2: 7 (mSUGRA)

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

19. General Features of Mirage Mediation Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05 • Compressed Sparticle Mass Spectrum • small m parameter (~M1)  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)

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

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. Life is not so easy!Moduli-induced Gravitino Problem Endo,Hamaguchi,Takahashi 06 Nakamura,MY 06 cf. Joichi-MY ‘95 • 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 ~106 GeV to escape overclosure constraint. (wino case) Even severer constraint on gravitino mass for other neutralino case

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. Cosmology Highlightaxino 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. Phenomenology Highlights Nakamura,Okumura,MY 08, and work in progress • 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

26. Summary • 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?