-
Universal extra dimensions
All Standard Model fields propagate in the extra
dimension(s)
Translation invariance => momentum conservation
e.g. 〈φnφmφl 〉 ∝ δn+m+l ,0 φn : n-th KK excitation of φ
No tree-level contribution to SM processes involving only
0-modes
However chirality => orbifolding e.g. S1 (circle) → S1/Z2
(interval)=> translation invariance is broken
But KK-parity remains : KK-number even/odd → KK-parity +/-1=>
lightest KK-odd particle is stable
All SM gauge bosons have internal components AM ,M = 0 . . .D −
1- one gets eaten to give mass to 4d KK-vectors
- the remaining D − 5 form adjoint scalars (no extra scalar in D
= 5)
I. Antoniadis (Extra dimensions) 21 / 44
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Orbifolds
S1 : y ≡ y + 2πR / y → −y −→ S1/Z2
R0 πR 0 πR
Z2 acts also on fermion chirality (L→ L,R → −R) => 4d chiral
0-modes
Fields can be even or odd under Z2
Z2 even : Φe(xµ, y) =
∑
nΦ(n)e (x) cos
nRy
Z2 odd : Φo(xµ, y) =
∑
nΦ(n)o (x) sin
nRy
Odd fields have no 4d zero-modes
I. Antoniadis (Extra dimensions) 22 / 44
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Mass spectrum
Radiative corrections => mass shifts that lift degeneracy at
lowest KK level
divergent sum over KK modes in the loop => cutoff scale Λ ≃
10/R
I. Antoniadis (Extra dimensions) 23 / 44
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Lightest KK Particle (LKP)
1st KK of hypercharge boson Bµ1 in D = 5 or adjoint scalar B1H
in D = 6
I. Antoniadis (Extra dimensions) 24 / 44
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UED hadron collider phenomenology
large rates for KK-quark and KK-gluon production
LHC: 1-100 pb for R−1
-
Production at hadron colliders
I. Antoniadis (Extra dimensions) 26 / 44
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SUSY vs UED signals
Example: jet dilepton final state [25]
SUSY UED
I. Antoniadis (Extra dimensions) 27 / 44
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microgravity experiments
change of Newton’s law at short distances
detectable only in the case of two large extra dimensions
new short range forces
light scalars and gauge fields if SUSY in the bulk
or broken by the compactification on the brane
such as radion and lepton number
volume suppressed mass: (TeV)2/MP ∼ 10−4 eV → mm rangecan be
experimentally tested for any number of extra dimensions
- Light U(1) gauge bosons: no derivative couplings
=> for the same mass much stronger than gravity: >∼
106
I. Antoniadis (Extra dimensions) 28 / 44
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Experimental limits on short distance forces
V (r) = −G m1m2r
(
1 + αe−r/λ)
Radion ⇒ M∗ >∼ 6 TeV 95% CL Adelberger et al. ’06
I. Antoniadis (Extra dimensions) 29 / 44
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improved bounds in the range 5-15 µm
Geraci-Smullin-Weld-Chiaverini-Kapitulnik ’08
1 10 100 100010
-2
10-1
100
101
102
103
104
105
106
107
108
109
1010
Excluded by
experiment
Lamoreaux
U.Colorado
Stanford 2
Stanford 1
U.Washington 2
gauged
B#
Yukawa messengers
dilaton
KK gravitons
strange
modulus
gluon
modulus
heavy q
moduli
Stanford 3
α
λ (µm)
U.Washington 1
I. Antoniadis (Extra dimensions) 30 / 44
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Cantilever resonance (f0): ~300 Hz
Drive frequency(f0/3): ~100Hz
motion
Cantilever resonance (f0): ~300 Hz
Drive frequency(f0/3): ~100Hz
motion
z
x
y
Piezo actuator
(+/- 120 µm at f /3)0
Fiber
Drive mass
T est mass
Cantilever
Silicon nitride
shield (cutaway)
I. Antoniadis (Extra dimensions) 31 / 44
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improved bounds from Casimir effect in the nm range
Decca-Fischbach et al ’07, ’08
5: Colorado 4: Stanford 3: Lamoureaux 1: Mohideen et al.
I. Antoniadis (Extra dimensions) 32 / 44
-
I. Antoniadis (Extra dimensions) 33 / 44
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Neutron scattering:
bounds in the range
∼ 1pm - 1nm
Nesvizhevsky-Pignol-
Protasov ’07
[m]λ-1210 -1110 -1010 -910 -810 -710
|2lo
g|g
-26
-24
-22
-20
-18
-16
-14
-12
-10
-8
Random potential model
Comparing forward and backward scattering
Comparing forward scattering and total X-section
Asymmetry of scattering on noble gases
EXCLUDED
REGION
antiprotonic atoms
Ederth
Mohideen
Purdue
Unseen extra U
CN
gravitational level
gauge boson
in extra dimensions
Electroweak scale new boson
LIMITS ON EXTRA YUKAWA FORCE mass [eV]
110210310410510
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Neutron whispering gallery
Centrifugal quantum states of neutrons
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Randal Sundrum models
spacetime = slice of AdS5 : ds2 = e−2k|y |ηµνdx
µdxν + dy2 k2 ∼ Λ/M35
UV-brane IR-brane
y = 0 y = rc
MP MW−|Λ|
bulk
fine-tuned tensions: T = −T ′ = 24M35k
exponential hierarchy: MW = MPe−2krc M2P ∼ M35/k
M5 ∼ MGUT
4d gravity localized on the UV-brane, but KK gravitons on the
IR
I. Antoniadis (Extra dimensions) 36 / 44
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main prediction: spin-2 resonances at the TeV scale
mn = cn k e−2krc ∼ TeV cn ≃ (n + 1/4) for large n
=> spin-2 TeV resonances in di-lepton or di-jet channels
weakly coupled for mn < M5 e−2krc => k < M5
viable models: SM gauge bosons in the bulk, Higgs on the
IR-brane
AdS/CFT duals to strongly coupled 4d field theories
composite Higgs models, technicolor-type gYM = M5/k > 1
I. Antoniadis (Extra dimensions) 37 / 44
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RS2
IR-brane can move to infinity: rc →∞
M2P = M3 1−e−2πkrc
k← internal volume V finite =>
• always 4d gravity localized on the UV-brane
potential: 1r+ 1
k2r3← deviations (rc →∞)
k−1 108 GeV, T 1/4 > 1 TeV
I. Antoniadis (Extra dimensions) 38 / 44