Document

超弦理論的現象論
山口昌弘
（東北大学）
研究会超弦理論と宇宙＠尾道
２００８年2月１１～13日
Talk Plan
• Introduction : Flux compactification and
KKLT set-up
• Naturalness Problem of Weak Scale
• Warped Superstring Compactification
• SUSY phenomenology: mirage mediation
2
String Theory
Candidates for
1) Quantum Gravity
2) Ultimate Unified Theory
–
–
–
–
gauge structure
matter representations
generations
Yukawa couplings
They are sensitive to details of compactification. Probably premature…..
– origin of weak scale
supersymmetry breaking/ warped extra dimensions …
To me, this is less sensitive to details of compactification. Hope to get
some insight.
 I will discuss possible implications to TeV scale physics.
“String (inspired) phenomenology”
3
Moduli Stabilization:
A long-standing problem
• Moduli/Dilaton Stabilization
– Moduli have not been stabilized at tree level.
– Non-perturbative effects important
• Why moduli?
– structure of compact dimensions
– gauge & matter structure
• if light moduli
– SUSY breaking
– Cosmological implications
4
Gaugino condenstate:
runnaway potential
exponetial superpotential
 runaway scalar potential
V
Re S
How to avoid runaway?
race track : multiple gaugino condensates
non-perturbative corrections to Kaehler potential
………
5
Flux Compactificatons
• Switch on Fluxes: H(3) and F(3)
type IIB
side
• Consistent solution
• Complex moduli & dilaton are stabilized
6
• 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
7
 superpotential for complex moduli (z) and dilaton (t)
• Consistent solution for flux compactifications in IIB
– fluxes  warped throat (Klebanov-Strassler throat) Giddings-KachruPolchinski 02
– W stabilizes complex moduli as well as dilaton
– Kaehler moduli are not stabilized by fluxes
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
• Constant term in Superpotential
 simplest way to avoid runnaway behavior
• T modulus stablilized but with SUSY AdS vacuum
(Re T)
10
• Up-lifting of the scalar potential
– Adding SUSY breaking sector
– Minkowski, SUSY broken vacuum
(Re T)
– KKLT: anti-D3 on top of warped throat
– Dynamical SUSY breaking sector on D-branes can
also be OK
11
Naturalness of Weak Scale
• Why is weak scale much smaller than Planck scale?
• How is weak scale stabilized against radiative
corrections?
• Proposed Solutions:
– Low energy supersymmetry
– Large/Warped extra dimensions
– Unknown strong dynamics
…..
• Ingredients in string theory. Question is which plays a
crucial role.
12
KKLT: A Platform of TeV Phenomenology
Warped Extra Dimension
& Low Energy SUSY
Similar set-up with different flux configurations and SMbrane configuration
Macroscopically (phenomenologically) important
information: w_0, warp factor
 warped extra dim.
and
large w_0
strong warping
low-E SUSY
small w_0
mild warping
13
LHC (Large Hadron Collider) Experiment
pp collider at CERN
Center of mass energy =14 TeV
Starts 2008 (this year!)
Expects new physics discovery at TeV scale
14
Warped Superstring Compactification
at LHC
Noguchi, Yamashita &MY 04
Shiu et al 07
Yamashita, 08
15
Warped Extra Dimension
• 4+1 spacetime theory gives
a solution to the large hierarchy
Randall-Sundrum (’99)
– The extra dimension with finite size
– Massive objects
• A pair of branes with opposite tension
• Cosmological constant   0
– SM-brane is located at
a end of the extra dimension
• Solution is AdS5
T
SM-Brane
ds 2  e2 f ( y ) dx  dx  dy 2
Warp factor
SM metric with
Poincare symmetry
16
A stringy realization
Giddings-Kachru-Polchinski ‘02
Use of Klebanov-Strassler (KS)
geometry
– Deformed conifold
KS throat is glued into some
CY to give finite 4D gravity
17
•
•
How do we learn geometry of WED ?
– Kaluza-Klein modes: function on extra dimension manifold
 Properties of manifold
Kaluza-Klein (KK) modes
– Gravitational field

h
(
x
, y)
propagates extra dimensions:

hˆ  ( x  , y)   h( n) ( x  )  ( n) ( y)
(m)
(n)
mn
d
y
g

(
y
)

(
y
)



•
KK modes as a probe of extra dimensions
– Momentum along extra dim. KK Mass
( n)
– Amplitude  ( y)  KK couplings to SM-brane
•
Wavefunction of KK mode: localized nearby IR region
– sensitive to IR properties of warped throat
18/13
• KK modes can be observed
at collider experiments
gg, qq  KK  ll
– Seen as resonances
in Drell-Yan process
– Resonance:
position, width, height
 Mass, coupling etc
cf. Davoudiasl et al. (2000)
19/13
Warped Extra Dimensions
Warped superstring solution
À La String Theory
in type-IIB superstring:
Giddings, et al. (’03)
• Manifold is of Planck-size volume Klebanov-Strassler (2000)
– Realistic gravitational coupling
x
• KS-throat glued to a CY-space
KS-Throat
• The warped metric generated
by anti-symmetric F3 and H3
– Supersymmetry
– Moduli stabilization
SM-Brane
• Standard model brane at the apex of the conifold
20/13
Warped Extra Dimensions
À La String Theory
• Deformed Conifold
Conical 6 dimensional manifold
– The singularity is removed
by  with finite size S^3
– S 2  S 3 as its intersection
– S^3 squashes as tau grows
SM-brane
Infrared (IR)
t
Ultraviolet
(UV)
21/13
•
Warped Extra Dimensions
Warping generated by fluxes
À La String Theory
~
M   3 F(3)
– F3 going through S^3
S
–  H3 and F5 generated
~
~
H (3)  d B( 2) F(5)  B( 2)  F(3)
t
• From the solution for Einstein’s Eq.
Radial dependence
of warp factor
SM metric with
Poincare symmetry
– Poincare symmetry on SM-brane
– Warp factor is asymptotically AdS
( gs : Dilaton VEV,  : String length)
KS
AdS
0.8
measure_on_rs
Warp factor
0.6
0.4
t
0.2
0
0
2
4
6
8
10
tau
SM-brane
located here
22/13
•
Warped Extra Dimensions
Angular direction for extra dim.
À La String Theory
Angular
directions
Where
g m : One-forms for angular coordinates
 : Deformation Parameter,
determined by flux ratio
Angular
directions
23/13
Form of the Wave functions
1st Mode
2nd Mode
5th Mode
24/13
Numerical Results
• Mass and coupling for angular modes
25/13
Comparison with RS model
Coupling Universality is Violated in stringy realization
Mass spectrum is busier.
Two geometries are distinguishable experimentally.
KK modes are sensitive probe of IR region of warped throat.
26
Implication to Low E SUSY
27
Implications to Low-E SUSY
• Original Motivation of KKLT:
realization of dS vacuum in string theory
• Simple KKLT set-up can also provide a new
mediation mechanism of SUSY breaking.
Choi-Falkowski-Nilles
-Olechowski-Pokorski 04,05
Endo-MY-Yoshioka 05
Choi-Jeong-Okumura 05
.........
• mixed modulus anomaly mediation
= mirage mediation
28
Phenomenology with KKLT-like model
SUSY breaking sector added to uplift potential
Overall SUSY breaking characterized by gravitino mass:
SUSY breaking effect of Moduli T:
suppressed by one-loop factor
29
Gaugino Masses
Consider SM on D7 brane
Gauge kinetic function
Gaugino Mass
@GUT scale
moduli+anomaly mediation:
two contributions comparable
30
Gaugino Masses
For R~35 (KKLT),
M1: M2: M3~1 : 1.3: 2
cf.
M1: M2: M3~1: 2: 7
(mSUGRA)
31
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
32
General Features of Mirage Mediation
• Compact Sparticle Mass Spectrum
• small  parameter (~M1)
Endo-MY-Yoshioka 05
Choi-Jeong-Okumura 05
 small gluino mass/ RGE
• LSP(lightest superparticle): 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)
33
Mass Spectrum: Case Study
Endo,MY,Yoshioka 05
n=1,l=1/3
n=3,l=0
(KKLT)
34
Cosmological Embarrassment?
Gravitino Over-Production
• Moduli is relatively heavy ~107 GeV
 no cosmological moduli problem…?
• Gravitino is also heavy ~105 GeV
 no gravitino problem …?
• However,
“Gravitino Over-Production by Moduli Decay”
35
Gravitino Pair Production by Moduli Decay
Br(X  G3/2 G3/2) ~0.01
Endo,Hamaguchi,
Takahashi 06
Nakamura&MY 06
– essentially decay into “Goldstinos”
– proportional to Fx (SUSY breaking of X)
– effect overlooked for more than 10 years
(contribution suppressed for minimal Kaehler potential)
• BBN is OK if gravitino mass is heavier than ~ 50
TeV
• Most serious is over-abundance of neutralino
DM produced by gravitino decay
36
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 might
be disfavored in the presence
of moduli. (unstable gravitino)
37
Ways Out?
• lighter LSP (such as axino)
– how to realize lighter LSP? in particular within modulus-anomaly
mediation
 Nakamura-Okumura-MY, to appear
• Stable Gravitino:
(Asaka,Nakamura&MY 06)
– Constraint on gravitino relic abundance: less constrained
– possibility of gravitino warm dark matter
– give up moduli-anomaly mediation?
• Dilution by entropy productionthermal inflation
(Lyth & Stewart 96)
• Raising Gravitino Mass by Warped Configuration (Luty)
– AMSB may be suppressed by warped factor
– sensitive to radion stabilization
– light radion?  may cause another cosmological trouble
• To overcome the moduli-induced gravitino problem is crucial for
mixed moduli anomaly mediation (mirage mediation)
under investigation….
38
Conclusions
•
•
•
•
Moduli Stabilization: Flux compactification
Implications to Weak Scale Stabilization
warped superstring compactification
low-E SUSY: mirage mediation
• LHC will provide crucial information
beyond SM, and hopefully structure of
unified theory.
39
Stay Tuned!
40

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