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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

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


S. Nakamura & MY hep-ph/0602081


T. Asaka, S. Nakamura & MY, hep-ph/0604132


  • 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
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
talk plan
Talk Plan
  • Flux Compactifications
    • Moduli Stabilization
    • KKLT set up
  • Phenomenology
    • moduli+anomaly mediation (mirage mediation)
  • Cosmology
    • Overproduction of gravitinos by moduli decay
2 flux compactifications
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)
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

 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


Polchinski 02

kklt set up
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
Kaehler potential:
  • superpotential:
  • Assume in Planck unit (low-energy SUSY)

(Note: runaway potential if )

  • Potential minimum:
  • moduli mass  100 times heavier than gravitino
However the vacuum is SUSY AdS
  • One needs to add something to obtain flat Minkowski (vanishing potential energy)
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)

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

  • Many possible vacua with different sets of fluxes
  • No principle (so far) to single out a particular vacuum
many possibilities to phenomenology
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

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


small susy breaking scale
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

exponetial superpotential
  • runaway scalar potential

How to avoid runaway?


Re T

A way to avoid runway:

add constant to superpotential

flux compactification in type IIB superstring

Small SUSY breaking scale  small w_0

cancellation among big numbers???


  • 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.
3 phenomenology
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

phenomenology with kklt like model
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


Gaugino Masses

@GUT scale

moduli+anomaly mediation:

two contributions comparable

sparticle mass spectrum
Sparticle Mass Spectrum

Gaugino Masses

For RbX~35,

M1: M2: M3~1 : 1.3: 2


M1: M2: M3~1: 2: 7


mass scales little hierarchy
mass scales: little hierarchy
  • soft masses
  • gravitino mass
  • moduli mass
mirage mediation
mirage mediation

Choi, Jeong, Okumura 05

RG properties: Gaugino masses (as well as scalar masses) are unified at a mirage scale.


Lebedev, Nilles,

Ratz 05

general features of mixed modulus anomaly mediation or mirage mediation
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)
mass spectrum case study
Mass Spectrum: Case Study

Endo,MY,Yoshioka 05




recent developments
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

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

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

moduli decay into gravitino pair
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:


Decay amplitude

helicity ½ component

 enhancement

(no such enhancement for helicity 3/2)

Nakamura-MY 06

Endo,Hamaguchi,Takahashi 06

Decay Rate


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

note decay into other particles
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


-Takahashi 06

Dine et al 06

Summary Sheet on Moduli Decay

total decay rate

 reheat temperature

decay rate into gravitino pair

 branching ratio into gravitino

cosmology of heavy moduli scenario
Cosmology of Heavy Moduli Scenario

Nakamura-MY 06


-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


1) BBN constraint on gravitino decay

2) Overclosure (LSP overproduction)


Constraints from BBN


-Moroi 04

Gravitino yield from moduli decay

  • BBN constraint pushes gravitino

heavier than ~ 105 GeV

constraint from lsp abundance
Constraint from LSP abundance


  • 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


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)

ways out
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)
thermal inflation in mirage mediation
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


remark gravitino production from inflaton decay
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
5 summary
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)