Gary Shiu University of Wisconsininsti.physics.sunysb.edu/ITP/conf/YITPat40/talks/Shiu.pdf · 2007-05-05 · Gary Shiu University of Wisconsin YITP@40 Symposium. YITP’s “Theory

String Phenomenology

Gary ShiuUniversity of Wisconsin

YITP@40 Symposium

YITP’s “Theory Space”

Strings/SUGRA

YITP

QCD/Collider Physics

Standard Model & Beyond

Cosmology

Statistical Mechanics

Neutrinos

+ a lot more ...





How do we test these ideas?

Cosmic Microwave Background

• Almost scale invariant, Gaussian primordial spectrum predicted by inflation: good agreement with data.

• A tantalizing upper bound on the energy density during inflation:

V ! M4GUT ! (1016GeV)4 i.e., H ! 1014GeV

WMAP

WMAP & Beyond

Can we learn from the CMB (or other cosmological measurements) details of string compactification?

LHC & Beyond

Can we learn from the LHC (and beyond) details of string compactification?

Flux Compactification

Energy !

1

8!

!

"

E2 + B

2#

Various p!cycles of M

Vn1,n2,···,nk(!i) ! moduli lifted

nj =

!!j

F

!j

Analogous to turning on a B-field:

Energy cost depends on detailed geometry:

W =

!M

G ! ΩIn Type IIB: Gukov, Vafa, Witten

[Dasgupta, Rajesh, Sethi]; [Greene, Schalm, GS]; [Giddings, Kachru, Polchinski]

Warped Throats

5UV

AdSIR

Klebanov, Strassler

e.g., warped deformed conifold

Fluxes back-react on the metric:

leads to Randall-Sundrum hierarchy Giddings, Kachru, Polchinski

Warped Throats

5UV

AdSIR

Klebanov, Strassler

e.g., warped deformed conifold

Fluxes back-react on the metric:

leads to Randall-Sundrum hierarchy Giddings, Kachru, Polchinski

A variety of warped throats with different isometries and IR behavior.

Standard-like D-brane Models

Marchesano, GS; Verlinde, Wijnholt;Cascales, Garcia del Moral, Quevedo, Uranga;Blumenhagen, Cvetic, GS, Marchesano; ...

Brane InflationDvali and Tye

...

Reviews:[Quevedo, hep-th/0210292];[Burgess, hep-th/0606020];[Tye, hep-th/0610221];[Cline, hep-th/0612129];[Kallosh,hep-th/0702059], ...

DD Inflation

Brane Inflation in Warped Throats

D3D3

Brane Inflation in Warped Throats

Slow-roll

D3D3

Brane Inflation in Warped ThroatsSilverstein, TongDBI

D3D3


D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$


D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$

!2 ! f(!)!1Speed limit:


D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$

! =1

!

1 ! f(")"2

!2 ! f(!)!1Speed limit:

Non-Gaussianities

0.20.4

0.60.8

0.2

0.4

0.6

0.8

0

0.1

0.2

0.20.4

0.60.8

0.20.4

0.6

0.8

0.2

0.4

0.6

0.8

0

1

2

3

0.20.4

0.6

0.8

Large 3-point correlations that are potentially observable.

Moreover, distinctive shape.

Slow-roll DBI

[Figures from Chen, Huang, Kachru, Shiu]

(fNL ! !) (fNL ! !2)

Non-Gaussianities

0.20.4

0.60.8

0.2

0.4

0.6

0.8

0

0.1

0.2

0.20.4

0.60.8

0.20.4

0.6

0.8

0.2

0.4

0.6

0.8

0

1

2

3

0.20.4

0.6

0.8

Large 3-point correlations that are potentially observable.

Moreover, distinctive shape.

Slow-roll DBI

[Figures from Chen, Huang, Kachru, Shiu]

−54 < fNL < 114 (WMAP3) fNL ∼ 5 (PLANCK)

(fNL ! !) (fNL ! !2)

Probing the Warped Geometry

Exact KSMass Gap

AdSSpectral index depends on warp factor through:

GS, B. Underwood, PRL

Exact KS

Mass GapAdS

Probing the Warped Geometry

GS, B. Underwood, PRL

Running of spectral index:

Exact KS

AdS

Warped throats at the LHC & Beyond

Search for Warped KK GravitonsGS, Underwood, Walker, Zurek (to appear)

Much work on LHC signatures of KK gravitons for RS:

Davoudiasl, Hewett, Rizzo; Fitzpatrick, Kaplan, Randall, Wang; Agashe, Davoudiasl, Perez, Soni; ...

Couplings to KK gravitons only TeV suppressed

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)


In comparison to RS, the KS geometry has:


• Smaller KK spacingIn comparison to RS, the KS geometry has:


• Smaller KK spacing

• Stronger & mode-dependent couplings



• Smaller KK spacing

• Stronger & mode-dependent couplings


KK Gravitons: Production and Decay

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)

Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidalcurves. The symbols Cµ!,"#, Dµ!,"#(k1, k2) and Eµ!,"#(k1, k2) are defined in Eqs. (A.10),(A.11) and (A.12) respectively. m!, mA and m$ are masses of the scalar, vector and

fermion. ! =!

23(n+2) , " =

!16#GN and $ is the gauge-fixing parameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)


fermion. ! =!

23(n+2) , " =


26

Production:g

g

KK

q

q

KK

Decay:

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)


fermion.!=!

23(n+2),"=


26

KK KK

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)


fermion.!=!

23(n+2),"=


26

KK

g

g

q, !+

q, !!

W, Z, !

W, Z, !

KK Gravitons: Production and Decay

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)


fermion. ! =!

23(n+2) , " =


26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)


fermion. ! =!

23(n+2) , " =


26

Production:g

g

KK

q

q

KK

Decay:

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)


fermion.!=!

23(n+2),"=


26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)


fermion.!=!

23(n+2),"=


26

KK KK

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)


fermion.!=!

23(n+2),"=


26

KK

g

g

q, !+

q, !!

W, Z, !

W, Z, !

KK Graviton Resonances

• Closer spacing between resonances

• Higher and broader peaks:

• Relative heights between different KK resonances! ! !

!4! ! "

!2MKK

Happy Birthday, YITP!

Documents

Gary Shiu University of Wisconsininsti.physics.sunysb.edu/ITP/conf/YITPat40/talks/Shiu.pdf · 2007-05-05 · Gary Shiu University of Wisconsin YITP@40 Symposium. YITP’s “Theory