1. 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

2. :
Gunnar Nordstrom
Uber die Moglichkeit das electromagnetiche Feld und das Gravitationsfeld zu vereiningen
Phys. Z. 15, : :
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

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

4. 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”) 5
GN=1/(MP)2 4

5. 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

7. 32? 7? 6? extra dimensions? Experiments can actually discover them!
String theory demands extra dimensions.
20sec

8. strong, weak, electromagnetic forces have comparable strengths
hierarchy of scales
10-17 cm
Electroweak scale
range of weak force
mass is generated (W,Z)
strong, weak, electromagnetic
forces have comparable strengths
10-33 cm
Planck scale
GN ~lPl2 =1/(MPl)2
1028 cm
Hubble scale
size of universe lu
16 orders of magnitude
puzzle 1m

9. 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

10. 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.

11. compactification Nima Arkani-Hamed Savas Dimopoulos Gia Dvali
hiding the extra dimensions (I)
compactification
Nima Arkani-Hamed
Savas Dimopoulos
Gia Dvali 1m

12. Gauss’s Law
If the n extra dimensions are compactified down to sizes R, then Gauss’s Law 1m

13. Kaluza-Klein modes If a spatial dimension is periodic then
the momentum in that dimension is quantized:
From our dimensions of view the KK modes get mass:
KK momentum
tower of states
(n is the mode number, for 2 extra
dimensions two modes etc…) p

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

15. 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

16. Infinite Randall - Sundrum G Mother brane Our world brane
5th dimension
Zero mode graviton is trapped
on the mother brane (Planck
brane)

17. gravity gets stronger at extremely high energies (or short distances).
(4+n)d gravity
it gets stronger at lower energies if
there are extra dimensions….
4d gravity
force strength
energy

18. Grand Unification Force Strength new gravity Higher Energy strong weak
electromagnetic
new
Higher Energy

19. gravity is so weak that we have never even seen a graviton.
gravitons
are the most robust probe of extra dimensions
gravity is so weak that we have never even seen a graviton.
F=GN
melectronmelectron r2 r
melectron
The gravitational attraction between two electrons is about 1042 times smaller than the electromagnetic repulsion.

20. Fermion or VB pairs at hadron or e+e- colliders
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

21. Collider Detector at Fermilab

23. graviton emission in particle collisions

24. graviton emission simulation:

25. concentric cylindrical layers
energy deposited from the particle debris
of the collision in the middle

26. “lego” event display

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

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

29. Lykken/Matchev/Burkett/Spiropulu
qqbar->g G (d=2, M=1TeV, s=1.8TeV)
[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/ ]
Lykken/Matchev/Burkett/Spiropulu

30. Case d=6
Only qqbar->g G (PYTHIA graviton process), d=6, M=1TeV, s=1.8TeV

31. qq  Gg LHC 100fb-1 8.5 TeV 6.8 TeV 5.8 TeV 5.0 TeV 900 GeV 700 GeV 54
1150 GeV
950 GeV 3
1400 GeV
1100 GeV 2
MS reach, Run II
MSreach,Run I n
[Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]
very very optimistic estimates
8.5 TeV
6.8 TeV
5.8 TeV
5.0 TeV

32. Monojet+missing energy: DØ limit

33. Monojet+missing energy: CDF
Expected number of gravitons for 84pb-1
Result very soon

34. e+e-  gG @L3 (GMSB analyses)
[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and cor. version: hep ph/ ]
(GMSB analyses)

35. Total cross section analysis
e+e-GZ
( a la Higgs analyses)
[Balazs, Dicus, He, Repko, Yuan, hep-ph/ , Z width]
[Cheung, Keung, hep-ph/ , recoil mass]
MET+jets n
sZG(pb) e
sZG95%(pb)
Ms(TeV) 2
0.64
0.56
0.29
0.60 3
0.08
0.56
0.30
0.38 4
0.01
0.55
0.30
0.29
L3: Phys. Lett. B470, 281 (1999)
Visible Mass analysis
ALEPH-CONF
Total cross section analysis

36. Monojet + missing energy: LHC reach
Ian Hinchliffe

37. Pair production via virtual graviton exchange
e.g 2
> 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)

38. Virtual exchange: dielectron and diphoton D0 limits

39. M(gg) = 574 GeV
cosq* = 0.86

40. Virtual exchange: diphoton CDF analysis

41. (anomalous Zgg couplings analyses,WW x-section,Zg)
e+e- gg,VV
Standard Model
Interference Term
Gravity
Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/ ] Agashe, Deshpande, Phys. Lett. B456, 60 (1999)

42. Two-photon measurements at LEP-II

43. Virtual Graviton Exchange
Summary LEP
184 GeV
189 GeV
Graviton Emission
202 GeV
e+e-  gG
e+e-  ZG
n=2
n=3
n=4
n=5
n=6
n=2
n=3
n=4
n=5
n=6 A D L3
1.28
0.97
0.78
0.66
0.57
0.35
0.22
0.17
0.14
0.12
1.38
1.02
0.84
0.68
0.58
1.02
0.81
0.67
0.58
0.51
0.60
0.38
0.29
0.24
0.21
Virtual Graviton Exchange
e+e-
m+m-
t+t- qq
f f gg WW ZZ
Combined ALL
0.66/ /0.55 (bb)
0.84/1.12 (<189) /1.00 A D L3 O
0.60/0.76 (ff) (<202)
0.87/1.07 (<189) /0.89 (VV)
0.61/0.68 (ff) (<189)

44. and neutral gauge boson excitations
RS phenomenology
1500 GeV KK graviton/ its tower of states at LHC
e+e-m+m-
500 GeV KK graviton/ its tower of states at a lepton collider
500 GeV KK graviton
and neutral gauge boson excitations
Davoudiasl, Hewett,Rizzo

45. A spin 2 graviton: Can we tell?
1.5 TeV graviton
in Randal Sundrum
at LHC

46. new accelerators for new physics
Large Hadron Collider (CERN, 2006)
Linear Collider (?,~2012)

47. 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

48. 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.

49. 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

50. 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

51. Nima Arkani-Hamed

52. think w a y different

53. : Eot-Wash Group Measured gravity at the sub-mm level (down 0.2 mm)
Adelberger
et al
Measured gravity
at the sub-mm level
(down 0.2 mm)

54. 1030 1023 PRL 86 1418 (2001) 10-10 Purdue (AFM experiment 2001)
Fischbach et al
1023
PRL (2001)
10-10

55. short range gravity measurements
l<150 mm
M*>4 TeV
C.D. Hoyle, Ph.D thesis
University of Washington, 2001

56. short range gravity measurements

58. (Price &Long)
100u

59. e+e-  ff Terms ~cos3q, ~cos4q make differential cross
(QED analyses)
e+e-  ff
Terms ~cos3q, ~cos4q make differential cross
sections a unique signature
For ff other than ee the integrated
interference term for scattering angles from 0 to p 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, LT,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/ – DY, Bhabha]
[Rizzo, Phys. Rev. D59, (1999) - Bhabha]

60. Bhabha scattering results
ALEPH,OPAL,DELPHI,L3 combined:
(Bourilkov hep-ph/ )
MS>1.26 TeV (l=+1)
Ms>960 TeV (l=-1)

62. Black Hole production
at high energy collisions (Banks et al., Dimopoulos et al. Giddings et al.)
L. BORISSOV

63. 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