Moduli: Stabilization, Phenomenology & Cosmology 山口 昌弘 （東北大学） Yamaguchi Masahiro (Tohoku university) 清華大学 Refs. M.Endo, MY & Yoshioka hep-ph/ (PRD72:015004,2005) S. Nakamura & MY hep-ph/ (PLB638:389,2006) T. Asaka, S. Nakamura & MY, hep-ph/ (PRDD74:023520,2006)

2 1.Introduction Moduli fields: –characterize size and shape of extra dimensions in superstring theory Why moduli important? –Structure of extra dimensions gauge & Yukawa structure … –light moduli SUSY breaking Cosmology

3 Moduli stabilization –long standing problem Flux compactifications –most of moduli are stabilized –new and important insights KKLT set-up –simple and interesting framework phenomenology & cosmological studies initiated

4 Talk Plan Flux Compactifications –Moduli Stabilization –KKLT set up Phenomenology –moduli+anomaly mediation (mirage mediation) Cosmology –Overproduction of gravitinos by moduli decay

5 2. Flux Compactifications Moduli: Difficulty in generating potentials for moduli –known mechanism: very limited gaugino condensate worldsheet instantons Recent developments –Calabi-Yau compactifications with fluxes (type IIB superstring theory)

6 IIB superstring –2-form potential (NS-NS, RR) –3-form field strength superpotential for IIB theory complex moduli quantization of fluxes (3,0) form Gukov-Vafa-Witten ’99

7  superpotential for complex moduli (z) and dilaton (  ) Consistent solution for flux compactifications in IIB –fluxes  warped throat –W stabilizes complex moduli as well as dilaton –Kaehler moduli are not stabilized by fluxes Giddinge-Kachru- Polchinski 02

8 KKLT set-up Potential for Kaehler moduli:  non-perturbative effects e.g. gaugino condensate on D7 brane case of single overall moduli: gauge kinetic function on D7: superpotential from gaugino condensate Kachru-Kallosh-Linde-Trivedi 03

9 Kaehler potential: superpotential: Assume in Planck unit (low-energy SUSY) (Note: runaway potential if ) Potential minimum: moduli mass  100 times heavier than gravitino

10 However the vacuum is SUSY AdS One needs to add something to obtain flat Minkowski (vanishing potential energy)

11 Up-lifting of the scalar potential –KKLT: anti-D3 on top of warped throat (Dynamical SUSY breaking sector on D-branes may also be OK)

12 overall moduli in KKLT: –mass: –SUSY breaking: Heavy Moduli: –generic feature if superpotential is generated by non- perturbative effects  interesting implications to phenomenology and cosmology Buchmuller-Hamaguchi-Lebedev-Ratz 04 Kohri-MY-Yokoyama 05 Choi-Falkowski-NiIlles-Olechowski 05 Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

13 Landscape Many possible vacua with different sets of fluxes No principle (so far) to single out a particular vacuum

14 Many possibilities to phenomenology KKLT set-up –with small constant term in superpotential –SM brane localized far from warped throat  low-energy SUSY with mirage mediation

15 KKLT set-up –with large constant term in W –with SM brane at the top of warped throat  warped extra dimensions a la RS model Many more scenarios Balance among the three terms  –Gravitino mass can be arbitrarily small. –different scenario from mirage mediation Kallosh-Linde

16 KK modes of Warped String compactification Geometry of warped throat: –Klebanov-Strassler geometry –very different from AdS5 in infra-red region –KK modes of graviton: localized at infra-red region  sensitive probe KK modes can be used as a probe to discriminate stringy compactification from RS model. Noguchi,Yamashita&MY, 05 Yamashita, in preparation

17 KK modes Mass and Coupling Coupling Universality is Violated cf. RS model Mass spectrum is busier. Two geometries are Distinguishable Experimentally

18 Small SUSY breaking scale ? Once we have low-energy SUSY, then EW scale is protected from radiative corrections. Q. Can we obtain small SUSY breaking scale? A. promising way: dimensional transmutation in string theory: gauge coupling is dynamical

19 exponetial superpotential  runaway scalar potential How to avoid runaway? V Re T

20 A way to avoid runway: add constant to superpotential

21 flux compactification in type IIB superstring Small SUSY breaking scale  small w_0 cancellation among big numbers??? Bousso-Polchinski At this moment we do not yet understand the ultimate reason of why SUSY breaking scale is much smaller than the fundamental scale (even if low-energy SUSY is correct). In the following, we consider the simplest KKLT set-up and examine phenomenological consequences.

22 3. Phenomenology motivation of KKLT: –realization of dS vacuum in string theory: cosmological interest KKLT set-up is also an interesting setting for low-energy SUSY –Cf: conventional thought Choi-Falkowski-NiIlles-Olechowski 05 Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

23 Phenomenology with KKLT-like model Consider the case where SM gauge sector is on a D7 brane with Gaugino scale moduli+anomaly mediation: two contributions comparable Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

24 Sparticle Mass Spectrum Gaugino Masses For R bX ~35, M 1 : M 2 : M 3 ~1 : 1.3: 2 cf. M 1 : M 2 : M 3 ~1: 2: 7 (mSUGRA)

25 mass scales: little hierarchy soft masses gravitino mass moduli mass

26 mirage mediation RG properties: Gaugino masses (as well as scalar masses) are unified at a mirage scale. Choi, Jeong, Okumura 05 from Lebedev, Nilles, Ratz 05

27 General Features of Mixed- Modulus-Anomaly Mediation (or Mirage Mediation) Compact Sparticle Mass Spectrum small  parameter (~M 1 )  small gluino mass/ RGE LSP: neutralino –admixture of gauginos and higginos 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

28 Mass Spectrum: Case Study n=1,l=1/3n=3,l=0 (KKLT) Endo,MY,Yoshioka 05

29 Recent Developments Extensions of model (relaxing R=35) e.g. Abe, Higaki, Kobayashi 05  and B  problem Choi, Jeong, Okumura 05 Choi, Jeong, Kobayashi, Okumura 05 Asaka, Yamaguchi (in preparation) little hierarchy problem Choi, Jeong, Kobayashi, Okumura 06 Kitano, Nomura 06 Collider signatures (LHC) Baer, Park, Tata, Wang 06 Kawagoe, Nojiri 06

30 4. Cosmology Cosmological implications: –cosmological moduli problem –modular inflation (not discussed here) moduli as inflaton

31 Cosmological Moduli Problem Coherent oscillation of moduli fields would dominate the energy density of the universe. Late decay  reheating of the universe  disaster for big-bang nucleosynthesis (BBN) Hope: may be OK if moduli is heavy (Moroi-MY-Yanagida 95) Coughlan et al 83 de Carlos-Casas-Quevedo-Roulet 93 Banks-Kaplan-Nelson 93

32 Life is not that easy! –Overproduction of neutralino LSPs from moduli decay efficient annihilation among LSPs is required moduli mass > GeV (sensitive to LSP nature) –Overprodution of gravitinos from moduli decay (Moroi-MY-Yanagida 95, Kawasaki-Moroi-Yanagida 96) Nakamura-MY 06 Endo-Hamaguchi-Takahashi 06

Moduli Decay into Gravitino Pair Lagrangian (in Planck unit) total Kaehler potential Nakamura-MY 06 Endo,Hamaguchi,Takahashi 06 Interaction of X with gravitino bi-linear Auxiliary field (SUSY breaking) expectation for moduli:

34 Decay amplitude helicity ½ component  enhancement (no such enhancement for helicity 3/2) Decay Rate Nakamura-MY 06 Endo,Hamaguchi,Takahashi 06

35 REMARKS Possibile mixing with SUSY breaking field (Polonyi field) Z Mass diagonalization is needed. Coupling of heavy “X” field with gravitino is suppressed if 1) absence of certain coupling (e.g. ZZX*) 2) sufficiently light Z These conditions are easily violated. Furthermore, light Z would cause conventional moduli (or Polony) problem. We do not consider this possible suppression. Dine-Kitano- Morisse-Shirman 06 couples to gravitino pair. scalar partner of goldstino

36 Note: Decay into other particles e.g. decay into gauge bosons & gauginos Note: gaugino mass is a function of moduli fielld Nakamura-MY 06 Endo-Hamaguchi -Takahashi 06 Dine et al 06 Decay Rate

37 Summary Sheet on Moduli Decay total decay rate  reheat temperature decay rate into gravitino pair  branching ratio into gravitino

38 Cosmology of Heavy Moduli Scenario Consider the case: moduli mass>> gravitino mass >> soft masses Assume that the LSP is a neutralino. Moduli decay into  SM particles  reheating  SM sparticles  LSPs  gravitinos  hadronic/EM showers: BBN  LSPs Constraints: 1) BBN constraint on gravitino decay 2) Overclosure (LSP overproduction) Nakamura-MY 06 Endo-Hamaguchi -Takahashi 06

39 Constraints from BBN Kawasaki-Kohri -Moroi 04 Gravitino yield from moduli decay  BBN constraint pushes gravitino heavier than ~ 10 5 GeV

40 Constraint from LSP abundance Gravitino  LSP –Overabundance of the LSPs Relic abundance of the LSPs –LSPs are produced by gravitino decay –Annihilation of LSPs –Annihilation is not very efficient at low temperature (later epoch)  lower bound on the gravitino mass

41 LSP abundance case study: LSP=neutral Wino (largest annihilation cross section) 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 Low energy SUSY may be disfavored in the presence of moduli. (unstable gravitino) Nakamura-MY 06

42 Ways Out? lighter LSP (such as axino) –how to realize lighter LSP? in particular within mirage mediation Stable Gravitino: (Asaka,Nakamura&MY 06) –Constraint on gravitino relic abundance: less constrained –possibility of gravitino warm dark matter –give up mirage mediation? Dilution by entropy production –thermal inflation (Lyth & Stewart 96)

43 Thermal inflation in mirage mediation Introduction of Singlet S (a la deflected anomaly mediation) Solution to  -B  problem in MSSM S field: very flat potential with TeV mass  flaton: Thermal inflation occurs - Dilutes the primordial moduli - Neutralino Dark matter: may come from the flaton decay, or moduli/graviitno decay Asaka-MY in preparation Pomaral-Rattazzi

44 REMARK: Gravitino Production from Inflaton Decay Inflaton decay into gravitino pair: proportional to Fx: model dependent modular inflation: (inflaton=moduli) severely constrained other inflation scenarios (chaotic inflation/new inflation/hybrid inflation) – somewhat model dependent (VEV of Fx) –very severe constraints on inflationary scenario Kawasaki-Takahashi-Yanagida 06 Asaka-Nakamura-MY 06

45 5. Summary flux compactifications + non-perturbative effects (a la KKLT) Interesting insights to phenomenology & cosmology SUSY breaking and Mediation: –moduli + anomaly mediation –mirage unification of soft masses Cosmology –Heavy Moduli/Gravitino alone do not solve cosmological moduli problem. –Gravitino overprodution from moduli decay Possible ways out: thermal inflation (  deflected mirage mediation)