2014 : extra dimensions centennial

from the Standard Model to extra dimensions

many “flavors” of extra dimensions

direct and indirect effects of extra dimensions at the TeV scale

current results and upcoming discoveries

Gunnar NordstromGunnar Nordstrom

Uber die Moglichkeit das Uber die Moglichkeit das electromagnetiche Feld und das electromagnetiche Feld und das Gravitationsfeld zu vereiningenGravitationsfeld zu vereiningenPhys. Z. Phys. Z. 1515, 504 , 504 19141914

:: ::

::

Abstract. It is shown that a unified treatment of the electromagnetic and gravitational fields is possible if one views the four dimensional space time as a surface in a five dimensional world

Thedor KaluzaThedor Kaluza Oscar KleinOscar Klein

Kaluza Th.Sitzungsber. Press.Akad.Wiss.Math K1 (1921) 966Klein O. Z.Phys. 37 (1926) 895

Kaluza and Klein started from 5-dim gravity and derived Kaluza and Klein started from 5-dim gravity and derived 4-dim gravity plus electromagnetism4-dim gravity plus electromagnetism

They compactified the 5th dimensionThey compactified the 5th dimensionaround a circle of radius Raround a circle of radius R

(“cylinder condition”)(“cylinder condition”)

RgxdM 53*

RgxdM 53*

]4

1[ 24

FFRgMxd P]

4

1[ 24

FFRgMxd P

55

44

GGNN=1/(M=1/(MPP))22

the Standard Modelthe Standard Model

a list of particles with their “quantum numbers”, about 20 numbers that specify the strength of the

various particle interactions, a mathematical formula that you could write on a

napkin.

20s

extra dimensions?6?7?32?

String theory demands extra dimensions.

Experiments can actually discover them!

20sec

10-33 cmPlanck scale

GN ~lPl2 =1/(M1/(MPlPl))22

10-17 cmElectroweak scale

range of weak forcemass is generated (W,Z)

strong, weak, electromagneticforces have comparable strengths

1028 cmHubble scale

size of universe lu

hierarchy of scales

16 orders of magnitudepuzzle

1m

signals from extra dimensionssignals from extra dimensions

in short range gravity observations in particle collision observations in astrophysical/cosmological observations

? what particles can move in that dimension

? how big is that dimension

? what is its shape

how do we see a hidden dimension?how do we see a hidden dimension?

ADD type of models: the extra dimension(s) are finite (i.e. compactified), the world is a “braneworld”, gravity (or SM singlets) propagate in the bulk. Hierarchy is generated by a large volume of the extra dimensions.

Direct emission/virtual exchange.

Universal (Yale) type of models : No branes. Momentum conservation; Pair production of KK excitations.

RS type of models: the extra dimension(s) are infinite. Hierarchy is generated from a strong curvature of the extra dimensional space.

Direct resonant production of the spin-2 states in the graviton KK tower.

Frameworks

compactificationcompactification

Nima Arkani-HamedSavas DimopoulosGia Dvali

hiding the extra dimensions (I)

1m

Gauss’s LawGauss’s Law

Rr r

1

1~)(

Rr 1

~)(

212

)4(

121

2)4(

nnnPl

nnnPl

R

mm

MrV

r

mm

MrV

Rr r

1

1~)(

Rr 1

~)(

212

)4(

121

2)4(

nnnPl

nnnPl

R

mm

MrV

r

mm

MrV

If the n extra dimensions are compactified down to sizes R, then Gauss’s Law

nnPl

nPlanck MRM

2

)4(2 ~

nnPl

nPlanck MRM

2

)4(2 ~

1m

Kaluza-Klein modesKaluza-Klein modes

If a spatial dimension is periodic then the momentum in that dimension is quantized:

R

np

R

np

From our dimensions of view the KK modes get mass:

2

220

2

R

nmm 2

220

2

R

nmm

pR

1R

1R

2R

2R

3R

3R

4R

4

0

R R

KK momentumtower of states

(n is the mode number, for 2 extradimensions two modes etc…)

fm 10~ 7,6

nm1~ 3

mm1~ 2

Km10~ 1 9

Rn

Rn

Rn

Rn

fm 10~ 7,6

nm1~ 3

mm1~ 2

Km10~ 1 9

Rn

Rn

Rn

Rn

Pick the effective (higher dimensional) Pick the effective (higher dimensional) Planck Scale at 1TeV, thenPlanck Scale at 1TeV, then

brane-worldsbrane-worlds

Standard Model particles are trapped on a brane and Standard Model particles are trapped on a brane and can’t move in the extra dimensionscan’t move in the extra dimensions

There could be There could be other branes which other branes which would look like would look like dark matter to usdark matter to us

hiding the extra dimensions (II)

Mother braneMother brane

GG

Our world braneOur world brane

Randall - SundrumRandall - SundrumRandall - SundrumRandall - Sundrum

Zero mode graviton is trappedZero mode graviton is trappedon the mother brane (Planckon the mother brane (Planckbrane) brane)

5th dimension5th dimension5th dimension5th dimension

InfiniteInfinite

gravity gets stronger at extremely high energies (or short distances).

forc

e st

ren

gth

energy

4d gravity

(4+n

)d g

ravi

ty

it gets stronger at lower energies ifthere are extra dimensions….

Grand Unification Fo

rce S

tren

gth

Higher Energy

electromagnetic

strong

weak

gravity

new

gravitonsgravitons

are the most robust probe of extra dimensions

gravity is so weak that we have never even seen a graviton.

The gravitational attraction between two electrons is about 1042 times smaller than the electromagnetic repulsion.

F=GF=GNN

melectronmelectron

r2

rmelectron melectron

graviton production in collider experiments:

graviton emission

graviton Exchange Fermion or VB pairs at hadron or e+e- colliders

Each KK-graviton state couplesto the wall with Planck supressedstrength

The number of KK-states ~(ER)

The sum over all KK-states is not MPl supressed but MPl(4+d)

supressed i.e. MEWK supressedso we have sizable cross sections

Collider Detector at Fermilab

graviton emission in particle collisionsgraviton emission in particle collisions

www.columbia.edu/~lab71

graviton emission simulation:

concentric cylindrical layers

energy deposited from the particle debrisof the collision in the middle

“lego” event display

Two events are graviton simulation and one is real CDF data: Can you pick the gravitons?

two events are real CDF data and one is graviton simulation; Can you pick the graviton?

Lykken/Matchev/Burkett/Spiropulu

)41(216161861

221141

1,

,1

36

3232

21

2

12

xyxxyxxxy

xxxxxyx

yxF

s

m

s

tF

sMgGqq

dt

dnS

S

[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291]

qqbar->g G (=2, M=1TeV, s=1.8TeV)

Case =6

Only qqbar->g G (PYTHIA 6.115 + graviton process), =6, M=1TeV, s=1.8TeV

qq Gg

900 GeV700 GeV5

1000 GeV850 GeV4

1150 GeV950 GeV3

1400 GeV 1100 GeV2

MS reach, Run II

MSreach,Run I

n

[Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]very very optimistic estimates

8.5 TeV6.8 TeV5.8 TeV5.0 TeV

LHC 100fb-1

Monojet+missing energy: DØ limit

Expected number of gravitons for 84pb-1Monojet+missing energy: CDF

Result very soon

4422222

12/

22/2

coscos)1(3)1()2()cos1(

)1(2)cos,(

2 )cos,(

)2/(32cos

xxxxxxx

xxf

sE

xxfM

s

sGee

dxd

d

D

e+e- G@L3

[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and cor. version: hep ph/9811291]

(GMSB analyses)

e+e-G

20.64

0.56

0.29

0.60

30.080.560.300.38

40.010.550.300.29

nZG(pb)

ZG

95%(pb)Ms(TeV)

MET+jets

[Balazs, Dicus, He, Repko, Yuan, hep-ph/9904220, Z width]

[Cheung, Keung, hep-ph/9903294, recoil mass]

L3: Phys. Lett. B470, 281 (1999)Visible Mass analysisALEPH-CONF-99-027

Total cross section analysis

( a la Higgs analyses)

2nfor /1066.1)(

8

1

ff

ff 47

2

Z

MnIM

M

Z

GZn

n 14 TeV100 fb-1

14 TeV1000 fb-1

28 TeV100 fb-1

28 TeV1000 fb-1

2 9 12 15 19

3 6.8 8.3 11.5 14

4 5.8 6.9 10 12

Ian Hinchliffe

Monojet + missing energy: LHC reach

Pair production via virtual graviton exchange

2e.g

> Gravity effects interfere with SM effects> 3 terms in the production cross section: SM, intrerference, gravity> the sum over the KK states is divergent anda cutoff is required (Ms)

Virtual exchange: dielectron and diphoton D0 limits

M() = 574 GeVcos* = 0.86

Virtual exchange: diphoton CDF analysis

e+e- VV

8

2

42

2

22

1

cos11

4

)cos1(

)cos1(

2)(

cos

T

T

O

s

see

d

d

Standard Model

Interference Term

Gravity

Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] Agashe, Deshpande, Phys. Lett. B456, 60 (1999)

)(2

)()( 4

1

4

1

4 GRWJHMADM TSS

(anomalous Z couplings analyses,WW x-section,Z)

Two-photon measurements at LEP-II

|)( JHMsMs

0.50 0.63

0.63 0.60

0.49 0.490.58 0.54

0.56 0.69

0.91 0.99

0.56 0.65

0.59 0.73

0.66/0.61 0.55/0.55 (bb)

0.57 0.59

0.63 0.68

0.80 1.03

qqee

ee ZGee G

0.58

0.68

0.66

n=5

0.60

0.35

n=2

0.38

0.22

n=3

0.29

0.17

n=4

0.24

0.14

n=5

1.02

1.38

1.28

n=2

0.81

1.02

0.97

n=3

0.67

0.84

0.78

n=4

0.51

0.58

0.57

n=6

0.21

0.12

n=6

202 GeV

189 GeV

184 GeV

Virtual Graviton Exchange

Summary LEP Graviton Emission

A

D

L3

A

D

L3

O 0.61/0.68 (ff) (<189)

0.87/1.07 (<189) 0.82/0.89 (VV)

0.60/0.76 (ff) (<202)

0.84/1.12 (<189) 0.75/1.00

Combined ALL

0.61 0.68

0.84 1.00

0.60 0.76

0.82 1.04

f f

0.63 0.64

0.76 0.77

0.68 0.79

0.80 0.79

0.69 0.71

0.91 0.92

ZZWW

Davoudiasl, Hewett,Rizzo

1500 GeV KK graviton/ its tower of states at LHC

500 GeV KK gravitonand neutral gauge boson excitations

e+e-

500 GeV KK graviton/ its tower of states at a lepton collider

RS phenomenology

A spin 2 graviton: Can we tell?

1.5 TeV gravitonin Randal Sundrumat LHC

Large Hadron Collider (CERN, 2006)

new accelerators for new physics

Linear Collider (?,~2012)

Plethora of new models that involve extra dimensions

Use Extra Dimensions Geomerty to solve:EWKBhierarchy problemSUSY Breakingflavor Breakingneutrino massesproton decay supressionGrand Unificationthe cosmological problem

More ideas are being explored

extra-new ideas

Deconstructing dimensions and sting theories:

The extra dimension(s) emerges from the theory, is well used, and then the theory comes back to the normal 4 dimensions serviced and healthy and with all the necessary Higgses. No tricks.

(Arkani-Hamed et al, Hill et al…..)

hiding the extra dimensions (III)no need to hide them

what is the physics that connects the gravitational scale and the scale of the typical mass of the elementary particles

what are the dimensions and dynamics behind spacetime

how is string theory connected to the world

If you ask questions about what happened at very early times, and you compute the answer, the answer is: Time doesn’t mean anything. S. Coleman

Space and time may be doomed. E. Witten

I am almost certain that space and time are illusions. N. Seiberg

The notion of space-time is clearly something we’re going to have to give up. A. Strominger

Nima Arkani-Hamed

Eot-WashEot-WashGroupGroup

Adelbergeret al

Adelbergeret al

::

Measured gravityat the sub-mm level(down 0.2 mm)

PRL 86 1418 (2001)PRL 86 1418 (2001)

12

12

2121 -exp 1

)()()( r

r

rrGdrdrrV N

10-10

1030

1023

Purdue (AFM experiment 2001)Fischbach et al

short range gravity measurements

C.D. Hoyle, Ph.D thesisUniversity of Washington, 2001

<150 mmM*>4 TeV

short range gravity measurements

100u

(Price &Long)(Price &Long)

e+e- ff

),(),(),(ff

2

44ts

Mts

MtsSMee

d

dGRV

sINTF

s

For ff other than ee the integrated interference term for scattering angles from 0 to is ZERO.The interference between graviton and t-channel SM Bhabha is giving sizable contributions good sensitivity

Terms ~cos3, ~cos4 make differential cross sections a unique signature

Every author and every experiment choose their Ms, T,sign conventions as different ap from the others...

(QED analyses)

[Hewett, Phys. Rev. Lett. 82, 4765 (1999) - DY] [Giudice, Rattazzi, Wells Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291 – DY, Bhabha][Rizzo, Phys. Rev. D59, 115010 (1999) - Bhabha]

11

1

41

2

RizzoS

HewettS

GRWT

HewettS

MM

M

Bhabha scattering results

ALEPH,OPAL,DELPHI,L3 combined:(Bourilkov hep-ph/9907380)

MS>1.26 TeV (=+1)

Ms>960 TeV (=-1)

Black Hole productionat high energy collisions (Banks et al., Dimopoulos et al. Giddings et al.)

L. BORISSOV

Collider Black Hole Production?

• If the Planck scale is the TeV scale, gravity becomes strong at the TeV scale : In high energy particle collisions short-lived microscopic black holes will be created

• These decaying black holes could be observed in future colliders, such as CERN’s LHC!

p

p

( bets?)