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Moduli: Stabilization, Phenomenology & Cosmology

Moduli: Stabilization, Phenomenology & Cosmology. 山口　昌弘 （東北大学） Yamaguchi Masahiro (Tohoku university) seminar @ 清華大学　 2006. 11. 24 Refs. M.Endo, MY & Yoshioka hep-ph/0504036 (PRD72:015004,2005) S. Nakamura & MY hep-ph/0602081

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Moduli: Stabilization, Phenomenology & Cosmology

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  1. Moduli:Stabilization, Phenomenology & Cosmology 山口　昌弘 （東北大学） Yamaguchi Masahiro (Tohoku university) seminar @清華大学　 2006. 11. 24 Refs. M.Endo, MY & Yoshioka hep-ph/0504036 (PRD72:015004,2005) S. Nakamura & MY hep-ph/0602081 (PLB638:389,2006) T. Asaka, S. Nakamura & MY, hep-ph/0604132 (PRDD74:023520,2006)

  2. 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 Gukov-Vafa-Witten ’99 (3,0) form

  7.  superpotential for complex moduli (z) and dilaton (t) • 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 Kachru-Kallosh-Linde-Trivedi 03 • 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

  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. 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

  17. exponetial superpotential • runaway scalar potential How to avoid runaway? V Re T

  18. A way to avoid runway: add constant to superpotential

  19. 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.

  20. 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

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

  22. Sparticle Mass Spectrum Gaugino Masses For RbX~35, M1: M2: M3~1 : 1.3: 2 cf. M1: M2: M3~1: 2: 7 (mSUGRA)

  23. mass scales: little hierarchy • soft masses • gravitino mass • moduli mass

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

  25. General Features of Mixed- Modulus-Anomaly Mediation (or Mirage Mediation) Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05 • Compact Sparticle Mass Spectrum • small m parameter (~M1)  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)

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

  27. Recent Developments Extensions of model (relaxing R=35) e.g. Abe, Higaki, Kobayashi 05 m and Bm 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

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

  29. Cosmological Moduli Problem Coughlan et al 83 de Carlos-Casas-Quevedo-Roulet 93 Banks-Kaplan-Nelson 93 • 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)

  30. Life is not that easy! • Overproduction of neutralino LSPs from moduli decay • efficient annihilation among LSPs is required • moduli mass >106-107 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

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

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

  33. REMARKS Dine-Kitano-Morisse-Shirman 06 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. couples to gravitino pair. scalar partner of goldstino

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

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

  36. Cosmology of Heavy Moduli Scenario Nakamura-MY 06 Endo-Hamaguchi -Takahashi 06 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)

  37. Constraints from BBN Kawasaki-Kohri -Moroi 04 Gravitino yield from moduli decay • BBN constraint pushes gravitino heavier than ~ 105 GeV

  38. 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

  39. LSP abundance case study: LSP=neutral Wino (largest annihilation cross section) Nakamura-MY 06 Gravitino mass must be heavier than ~106 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)

  40. 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)

  41. Thermal inflation in mirage mediation Asaka-MY in preparation Introduction of Singlet S (a la deflected anomaly mediation) Solution to m-Bm 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 Pomaral-Rattazzi

  42. REMARK: Gravitino Production from Inflaton Decay Kawasaki-Takahashi-Yanagida 06 Asaka-Nakamura-MY 06 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

  43. 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)

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