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the physics of extra dimensions
Maria Spiropulu
Enrico Fermi Institute/UofC
 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 Nordstrom
:
:
Uber die Moglichkeit das
electromagnetiche Feld und das
Gravitationsfeld zu vereiningen
Phys. Z. 15, 504 1914
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 Kaluza
Oscar Klein
Kaluza Th.Sitzungsber. Press.Akad.Wiss.Math K1 (1921) 966
Klein O. Z.Phys. 37 (1926) 895
Kaluza and Klein started from 5-dim gravity and derived
4-dim gravity plus electromagnetism
They compactified the 5th dimension
around a circle of radius R
(“cylinder condition”)
M*
3
d
x

g
R

5
GN=1/(MP)2
d
x
[
M
P

4
2
1

 g R  F F ]
4
the 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
e
 e 
e 
  e
u u u
d d d
u u u
  
 
  L
d d d
Z
0
W
W





c c c
s s s
c c c
t t t
b b b
t t t
s s s
t t t


  
 
 
  L
g
e
 e 
e 
  e
u u u
d d d
u u u
  
 
  L
d d d
Z
0
W
W





c c c
s s s
c c c
t t t
b b b
t t t
s s s
t t t


  
 
 
  L
g
e
 e 
e 
  e
u u u
d d d
u u u
  
 
  L
d d d
Z
0
W
W





c c c
s s s
c c c
t t t
b b b
t t t
s s s
t t t


  
 
 
  L
g
e
 e 
e 
  e
u u u
d d d
u u u
  
 
  L
d d d
Z
0
W
W





c c c
s s s
c c c
t t t
b b b
t t t
s s s
t t t


  
 
 
  L
g
what does the Standard Model not explain ?
 quantum gravity
HST image of an 800 light-year wide spiral shaped
disk of dust fueling a 1.2x10^9 solar mass black hole
in the center of NGC 4261
10s
what does the Standard Model not explain ?
 quantum gravity
 dark matter and dark energy
10s
what does the Standard Model not explain ?
 quantum gravity
 dark matter and dark energy
 Higgs
G.t’Hooft
10s
Arrange it so delicately that it will fall down in 19 minutes.
the Bigger Big picture
The Standard Model describes everything that we have
seen to extreme accuracy.
Michelangelo Antonioni on Ferrara:
“...it is a city that you can only see partly
and the rest disappears and can only
be imagined...” (beyond the clouds)
the Bigger Big picture
Now we want to extend the model to
higher energies and get the whole picture
For this we need new experiments and ideas
32?
7?
6? extra dimensions?
Experiments can actually
discover them!
String theory demands extra
dimensions.
20sec
hierarchy of scales
10-17 cm
10-33 cm
Planck scale
GN ~lPl2 =1/(MPl)2
Electroweak scale
range of weak force
mass is generated (W,Z)
strong, weak, electromagnetic
forces have comparable strengths
1028 cm
16 orders of magnitude
puzzle
Hubble scale
size of universe lu
1m
signals from extra dimensions
in short range gravity observations
 in particle collision observations
in astrophysical/cosmological observations
how do we see a hidden dimension?
? what particles can move in that dimension
? how big is that dimension
? what is its shape
Frameworks
 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.
 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.
 Universal (Yale) type of models : No branes. Momentum
conservation; Pair production of KK excitations.
hiding the extra dimensions (I)
compactification
Nima Arkani-Hamed
Savas Dimopoulos
Gia Dvali
1m
Gauss’s Law
If the n extra dimensions are compactified down to
sizes R, then Gauss’s Law
V (r ) ~
V (r ) ~
M
1
M Pln(24 n )
1
M Pln(24 n )
2
Planck
m1m2
r  R
n 1
r
m1m2 1
r  R
n
R r
n
~R M
2 n
Pl ( 4 n )
1m
Kaluza-Klein modes
If a spatial dimension is periodic then
the momentum in that dimension is quantized:
n
p
R
From our dimensions of view the KK modes get mass:
m 2  m02 
n2
R
2
(n is the mode number, for 2 extra
dimensions two modes etc…)
p
4
R
3
R
2
R
1
R
0
KK momentum
tower of states
 R
Pick the effective (higher dimensional)
Planck Scale at 1TeV, then
n 1

R ~ 10 Km
n2

R ~ 1mm
n3

R ~ 1nm
9

n  6,7 
R ~ 10 fm
hiding the extra dimensions (II)
brane-worlds
There could be
other branes which
would look like
dark matter to us
Standard Model particles are trapped on a brane and
can’t move in the extra dimensions
Infinite Randall - Sundrum
G
Mother brane
5th dimension
Our world brane
Zero mode graviton is trapped
on the mother brane (Planck
brane)
gravity gets stronger at extremely high
energies (or short distances).
it gets stronger at lower energies if
there are extra dimensions….
Grand Unification
gravity
Higher Energy
gravitons
are the most robust probe of extra dimensions
gravity is so weak that we have never
even seen a graviton.
melectronmelectron
F=GN
r2
melectron
r
melectron
The gravitational attraction between two electrons is
about 1042 times smaller than the electromagnetic
repulsion.
graviton production in collider experiments:
graviton emission
Each KK-graviton state couples
to the wall with Planck supressed
strength
The number of KK-states ~(ER)d
The sum over all KK-states is
not MPl supressed but MPl(4+d)
supressed i.e. MEWK supressed
so we have sizable cross sections
graviton Exchange
Fermion or VB pairs at hadron or e+e- colliders
Collider Detector at Fermilab
graviton emission in particle collisions
www.columbia.edu/~lab71
graviton emission simulation:
concentric cylindrical layers
energy deposited from the particle debris
of 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?
qqbar->g G (d=2, M=1TeV, s=1.8TeV)
[Giudice, Rattazzi, Wells,
Nucl. Phys. B544, 3 (1999)
and corrected version, hepph/9811291]
 t m2 
S 1
d
qq  gG  
F  , 
n2 1 
dt
36 sM S
s s 
F1 x, y  

y 1  6 x  18 x 2
Lykken/Matchev/Burkett/Spiropulu



 16 x   6 y x1  2 x   y (1  4 x)
1
 4 x1  x  1  2 x  2 x 2 
x y  1  x 
3
2
3
Case d=6
Only qqbar->g G (PYTHIA 6.115 + graviton
process), d=6, M=1TeV, s=1.8TeV
qq  Gg
n
MSreach,
Run I
MS reach,
Run II
2
1100 GeV
1400 GeV
950 GeV
1150 GeV
850 GeV
1000 GeV
700 GeV
900 GeV
[Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]
3
very very optimistic estimates
4
5
LHC
100fb-1
8.5 TeV
6.8 TeV
5.8 TeV
5.0 TeV
Monojet+missing energy: DØ limit
Monojet+missing energy: CDF
Expected number of gravitons for 84pb-1
Result very soon
e+e-  G
@L3
[Giudice, Rattazzi, Wells, Nucl.
Phys. B544, 3 (1999) and cor.
version: hep ph/9811291]
d 2
 s
d
 
2 E
 

 f ( x , cos )
e e  G 
x


s
dxd cos
32s (d / 2)  M D 
2(1  x)d / 21
2
2
2
2
4
4
f ( x , cos ) 
(
2

x
)
(
1

x

x
)

3
x
(
1

x
)
cos


x
cos

x(1  cos 2  )
2

d /2


(GMSB analyses)

e+e-GZ
Z  ff G  1

Z  ff  8
 MZ 


M
 
( a la Higgs analyses)
n2
7
I (n)  1.66 10 / M
4

for n  2
[Balazs, Dicus, He, Repko, Yuan, hepph/9904220, Z width]
[Cheung, Keung, hep-ph/9903294,
recoil mass]
MET+jets
n
ZG(pb)
e
ZG95%(pb)
Ms(TeV)
2
0.64
0.56
0.29
0.60
L3: Phys. Lett. B470, 281 (1999)
Visible Mass analysis
ALEPH-CONF-99-027
Total cross section analysis
3
0.08
0.56
0.30
0.38
4
0.01
0.55
0.30
0.29
Monojet + missing energy: LHC reach
Ian Hinchliffe
n
14 TeV
100 fb-1
14 TeV
1000 fb-1
28 TeV
100 fb-1
28 TeV
1000 fb-1
2
9
12
15
19
3
4
6.8
5.8
8.3
6.9
11.5
10
14
12
Pair production via virtual graviton exchange
2
e.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 and
a cutoff is required (Ms)
Virtual exchange: dielectron and diphoton D0 limits
M() = 574 GeV
cos* = 0.86
Virtual exchange: diphoton CDF analysis
(anomalous Z couplings analyses,WW x-section,Z)
e+e- ,VV
Standard Model
 2 (1  cos 2  )



2
(1  cos  )


4


2
d
2 
s  1 
 

 1  cos 2  
(e e   ) 


d cos 
s 
4  T 


8


 1 

 O 

Gravity


 T 
Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hepph/9811291] Agashe, Deshpande, Phys. Lett. B456, 60 (1999)
M S4
  1
( AD)  M
4
S
( JH )
  1

2

4 T (GRW )
Two-photon measurements at LEP-II
Ms  Ms ( JH ) | 
Summary LEP
184 GeV
189 GeV
Graviton Emission
202 GeV
ee  G
n=2 n=3 n=4 n=5 n=6 n=2
A 1.28
0.97
0.78
0.66
0.57
D 1.38
1.02
0.84
0.68
0.58
L3 1.02
0.81
0.67
0.58
0.51
ee  ZG
n=3 n=4 n=5
n=6
0.35
0.22
0.17
0.14
0.12
0.60
0.38
0.29
0.24
0.21
Virtual Graviton Exchange
ee   qq
ff
A

0.80
1.03
D
L3
O
0.91
0.99

0.63
0.68
0.59
0.73
0.56
0.69
0.63
0.60
0.57
0.59
0.56
0.65
0.58
0.54
0.50
0.63
0.66/0.61
0.55/0.55 (bb)
0.49
0.49
0.82
1.04
0.60
0.76
0.84
1.00
0.61
0.68

WW ZZ
0.91
0.92
0.69
0.71
0.80 0.68
0.79 0.79
0.63
0.64
Combined ALL
0.84/1.12 (<189)
0.75/1.00
0.60/0.76 (ff) (<202)
0.76
0.77
0.87/1.07 (<189)
0.82/0.89 (VV)
0.61/0.68 (ff) (<189)
RS phenomenology
1500 GeV KK graviton/ its tower of states
at LHC
e+e-
500 GeV KK graviton/ its tower of states
at a lepton collider
500 GeV KK graviton
and neutral gauge boson excitations
Davoudiasl, Hewett,Rizzo
A spin 2 graviton: Can we tell?
1.5 TeV graviton
in Randal Sundrum
at LHC
new accelerators for new physics
Linear Collider (?,~2012)
Large Hadron Collider (CERN, 2006)
Plethora of new models that involve extra dimensions
Use Extra Dimensions Geomerty to solve:
EWKB
hierarchy problem
SUSY Breaking
flavor Breaking
neutrino masses
proton decay supression
Grand Unification
the cosmological problem
More ideas are being explored
hiding the extra dimensions (III)
no need to hide them
extra-new ideas
(Arkani-Hamed et al, Hill et al…..)
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.
 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
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
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
Nima Arkani-Hamed
D. Gross
SCIENCE: The Glorious Entertainment
…for any important assertion evidence must be produced;
…prophecies and bugaboos must be subjected to scrutiny;
… guesswork must be replaced by exact count;
….accuracy is a virtue and inquiry is a moral imperative
To the hegemony of science we owe a feeling for which
there is no name, but which is akin to the faith of the
innocent that the truth will out and vindication will follow.
In its purest form science is justice as well as reason.
Jacques Barzun
:
Eot-Wash
Group
Adelberger
et al
Measured gravity
at the sub-mm level
(down 0.2 mm)
1030
1023
Purdue (AFM experiment 2001)
Fischbach et al
PRL 86 1418 (200
10-10
V (r )   dr1  dr2
GN  (r1 )  (r2 ) 
 - r12 
1


exp


 

r12
short range gravity measurements
C.D. Hoyle, Ph.D thesis
University of Washington, 2001
<150 mm
M*>4 TeV
short range gravity measurements
(Price &Long)
100u
1
(QED analyses)
+
ee
ff
 
d  

e e  ff  SM ( s, t )  4  INTF ( s, t )   4
 Ms
d
Ms



M SHewett
 2  4 GRW
   T
  1
 
M SHewett
 M SRizzo
  1
2

  GRV ( s, t )


Terms ~cos3, ~cos4 make differential cross
sections a unique signature
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
Every author and every experiment choose their
Ms, T,sign conventions as different ap from
the others...
[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]
  1
Bhabha scattering results
ALEPH,OPAL,DELPHI,L3 combined:
(Bourilkov hep-ph/9907380)
MS>1.26 TeV (=+1)
Ms>960 TeV (=-1)
Black Hole production
at 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!
( bets?)
p
p