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 　　　　　　　　　　　　　　　　　　 (PRD72:015004,2

005) S. Nakamura & MY hep-ph/0602081

(PLB638:389,2006) T. Asaka, S. Nakamura & MY, hep-ph/0604132

(PRDD74:023520,2006)

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1. Introduction

• Moduli fields:– characterize size and shape of extra dimensions in su

perstring theory

• Why moduli important?– Structure of extra dimensions

• gauge & Yukawa structure …– light moduli

• SUSY breaking• Cosmology

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• 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

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Talk Plan

• Flux Compactifications– Moduli Stabilization– KKLT set up

• Phenomenology– moduli+anomaly mediation (mirage mediation)

• Cosmology– Overproduction of gravitinos by moduli decay

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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)

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• 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

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　 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

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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

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

　　 (Note: runaway potential if )

• Potential minimum:

• moduli mass 100 times heavier than gravitino

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• However the vacuum is SUSY AdS

• One needs to add something to obtain flat Minkowski (vanishing potential energy)

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• 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)

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• overall moduli in KKLT:– mass:

– SUSY breaking:

• Heavy Moduli: – generic feature if superpotential is generated by non-p

erturbative effects

interesting implications to phenomenology and cosmology

Buchmuller-Hamaguchi-Lebedev-Ratz 04Kohri-MY-Yokoyama 05Choi-Falkowski-NiIlles-Olechowski 05Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05

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Landscape

• Many possible vacua with different sets of fluxes

• No principle (so far) to single out a particular vacuum

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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

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• 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

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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

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exponetial superpotential runaway scalar potential

How to avoid runaway?

V

Re T

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• A way to avoid runway:

add constant to superpotential

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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.

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3. Phenomenology

• motivation of KKLT:– realization of dS vacuum in string theory: cos

mological interest

• KKLT set-up is also an interesting setting for low-energy SUSY

– Cf: conventional thought

Choi-Falkowski-NiIlles-Olechowski 05Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05

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Phenomenology with KKLT-like model

Consider the case where SM gauge sector is on a D7 brane with

Gaugino Masses

@GUT scale

moduli+anomaly mediation: two contributions comparable

Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05

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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

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

Choi, Jeong, Okumura 05

from Lebedev, Nilles, Ratz 05

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General Features of Mixed- Modulus-Anomaly Mediation (or Mirage Mediation)

• Compact Sparticle Mass Spectrum• small 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)

Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05

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Mass Spectrum: Case Study

n=1,l=1/3 n=3,l=0(KKLT)

Endo,MY,Yoshioka 05

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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

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4. Cosmology

• Cosmological implications:

– cosmological moduli problem

– modular inflation (not discussed here)• moduli as inflaton

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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 83de Carlos-Casas-Quevedo-Roulet 93Banks-Kaplan-Nelson 93

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Life is not that easy!– Overproduction of neutralino LSPs from modu

li decay

• efficient annihilation among LSPs is required• moduli mass >106-107 GeV (sensitive to LSP natur

e)

– Overprodution of gravitinos from moduli decay

(Moroi-MY-Yanagida 95, Kawasaki-Moroi-Yanagida 96)

Nakamura-MY 06Endo-Hamaguchi-Takahashi 06

Moduli Decay into Gravitino Pair

Lagrangian (in Planck unit)

total Kaehler potential

Nakamura-MY 06Endo,Hamaguchi,Takahashi 06

Interaction of X with gravitino bi-linear

Auxiliary field (SUSY breaking)

expectation for moduli:

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Decay amplitude

helicity ½ component

enhancement

(no such enhancement for helicity 3/2)

Decay Rate Nakamura-MY 06Endo,Hamaguchi,Takahashi 06

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REMARKSPossibile 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

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Note: Decay into other particles

e.g. decay into gauge bosons & gauginos

Note: gaugino mass is a function of moduli fielld

Nakamura-MY 06Endo-Hamaguchi-Takahashi 06Dine et al 06

Decay Rate

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Summary Sheet on Moduli Decay

total decay rate

reheat temperature

decay rate into gravitino pair

branching ratio into gravitino

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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 06Endo-Hamaguchi-Takahashi 06

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Constraints from BBN Kawasaki-Kohri

-Moroi 04

Gravitino yield from moduli decay

BBN constraint pushes gravitino heavier than ~ 105 GeV

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Constraint from LSP abundance

GravitinoLSP

– 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 (lat

er epoch)

lower bound on the gravitino mass

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LSP abundance case study: LSP=neutral Wino (largest annihilation cross section)

Gravitino mass must beheavier than ~106 GeVto escape overclosureconstraint. (wino case)

Even severer constrainton gravitino mass for other neutralino case

Low energy SUSY maybe disfavored in the presenceof moduli. (unstable gravitino)

Nakamura-MY 06

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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)

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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

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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 06Asaka-Nakamura-MY 06

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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)