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)
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
2
• 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
3
Talk Plan
• Flux Compactifications
– Moduli Stabilization
– KKLT set up
• Phenomenology
– moduli+anomaly mediation (mirage mediation)
• Cosmology
– Overproduction of gravitinos by moduli decay
4
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)
5
• IIB superstring
– 2-form potential (NS-NS, RR)
– 3-form field strength
• superpotential for IIB theory
Gukov-Vafa-Witten ’99
(3,0) form
• complex moduli
• quantization of fluxes
6
 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-KachruPolchinski 02
7
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
8
• Kaehler potential:
• superpotential:
• Assume
in Planck unit (low-energy SUSY)
(Note: runaway potential if
)
• Potential minimum:
• moduli mass  100 times heavier than gravitino
9
• However the vacuum is SUSY AdS
• One needs to add something to obtain flat
Minkowski (vanishing potential energy)
10
• 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)
11
• overall moduli in KKLT:
– mass:
– SUSY breaking:
• Heavy Moduli:
Buchmuller-Hamaguchi-Lebedev-Ratz 04
Kohri-MY-Yokoyama 05
Choi-Falkowski-NiIlles-Olechowski 05
Endo-MY-Yoshioka 05
Choi-Jeong-Okumura 05
– generic feature if superpotential is generated by nonperturbative effects
 interesting implications to phenomenology and
cosmology
12
Landscape
• Many possible vacua with different sets of fluxes
• No principle (so far) to single out a particular vacuum
13
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
14
• 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
Kallosh-Linde
Balance among the three terms 
– Gravitino mass can be arbitrarily small.
– different scenario from mirage mediation
15
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
18
exponetial superpotential
runaway scalar potential
V
Re T
How to avoid runaway?
19
• A way to avoid runway:
add constant to superpotential
20
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.
21
3. Phenomenology
• motivation of KKLT:
– realization of dS vacuum in string theory:
cosmological interest
• KKLT set-up is also an interesting setting
05
for low-energy SUSY Choi-Falkowski-NiIlles-Olechowski
Endo-MY-Yoshioka 05
Choi-Jeong-Okumura 05
– Cf: conventional thought
22
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
23
Sparticle Mass Spectrum
Gaugino Masses
For RbX~35,
M1: M2: M3~1 : 1.3: 2
cf.
M1: M2: M3~1: 2: 7
(mSUGRA)
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mass scales: little hierarchy
• soft masses
• gravitino mass
• moduli mass
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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
26
General Features of Mixed- Modulus-Anomaly
Mediation (or Mirage Mediation)
• Compact Sparticle Mass Spectrum
• small m parameter (~M1)
Endo-MY-Yoshioka 05
Choi-Jeong-Okumura 05
 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)
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Mass Spectrum: Case Study
Endo,MY,Yoshioka 05
n=1,l=1/3
n=3,l=0
(KKLT)
28
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
29
4. Cosmology
• Cosmological implications:
– cosmological moduli problem
– modular inflation
(not discussed here)
• moduli as inflaton
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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)
31
Life is not that easy!
– Overproduction of neutralino LSPs from
moduli decay
(Moroi-MY-Yanagida 95,
Kawasaki-Moroi-Yanagida 96)
• efficient annihilation among LSPs is required
• moduli mass >106-107 GeV (sensitive to LSP
nature)
– Overprodution of gravitinos from moduli decay
Nakamura-MY 06
Endo-Hamaguchi-Takahashi 06
32
Moduli Decay into Gravitino Pair
Lagrangian (in Planck unit)
Nakamura-MY 06
Endo,Hamaguchi,Takahashi 06
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)
Decay Rate
Nakamura-MY 06
Endo,Hamaguchi,Takahashi 06
34
REMARKS
Possibile mixing with SUSY breaking field (Polonyi field) Z
couples to gravitino pair.
scalar partner of goldstino
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.
35
We do not consider this possible suppression.
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
36
Summary Sheet on Moduli Decay
total decay rate
 reheat temperature
decay rate into gravitino pair
 branching ratio into gravitino
37
Cosmology of Heavy Moduli
Nakamura-MY 06
Scenario
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)
38
Constraints from BBN
Kawasaki-Kohri
-Moroi 04
Gravitino yield from moduli decay
BBN constraint pushes gravitino
heavier than ~ 105 GeV
39
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
40
LSP abundance
Nakamura-MY 06
case study: LSP=neutral Wino
(largest annihilation cross section)
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)
41
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)
42
Thermal inflation in
mirage mediation
Asaka-MY in preparation
Introduction of Singlet S
(a la deflected anomaly mediation) Pomaral-Rattazzi
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
43
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
44
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)
45