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Physics of Extra Dimensions  A potential discovery for LHC/ILC . Abdel PérezLorenzana CINVESTAV. PASI2006, Puerto Vallarta. México. Introduction: Why considering Extra Dimensions? Dimensional reduction: The Effective Field Theory KK decomposition on torii and orbifolds
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Abdel PérezLorenzana
CINVESTAV
PASI2006, Puerto Vallarta. México.
Dimensional reduction: The Effective Field Theory
KK decomposition on torii and orbifolds
General phenomenological aspects
Gravitons Phenomenology
Phenomenology of XD matter fields
KK modes of Matter Fields: Universal Extra Dimensions
New Theoretical ideas for the use of XD
Program´
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Wonders from the XX centurywith matter in irrep
Theory of Everything??
Weak
EM
QG ??
Strong
The Unification SchemeWhile MGUT is calculable, the only plausible scale for Quantum Gravity seems to be the Planck Scale
Class FT
Relativistic Mech
GN 0
c 0
QFT
GN 0
GN 0
ħ 0
ToE[α(GN ,ħ,c)]
c 0
ħ 0
Gen Rel
c 0
ħ 0
Newtonian Mech
The Dream for a Unified TheoryThe best known candidate for the ToE is String Theory…
HE
Sugra D=10
String Theory needs extra compact spacelike dimensions to be consistent ( D=10 or D=11 for M Theory ).
S
T
S
HO
MTheory
Type II A
S
T
Ω
XD are compact and usually assumed to be
small
Type I
Type II B
L
Planck
String Theory and Extra DimensionsIn the Perturbative Heterotic String Theory Gravity and Gauge interactions have the same origin, as massless modes of the closed Heterotic String, and they are Unified at the String Scale
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Along the 80’s some authors (Antoniadis, Benakli, Quirós) suggested the possibility of having intermediate scales
11
M
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M
~
10
GeV
*
P
Recent developments on String Theory have given support to the idea that (some) extra dimensions could rather be larger than Planck length (HoravaWitten,´96)
ST
Can MString« MPlanck ?
The scale of STDpbrane
3brane
Open String
Closed String
( Gravity )
r
(Gauge)
R
Perperdicular XD
In 1998 ArkaniHammed, Dimopoulus and D’vali made the key observation that extra dimensions could even be of millimeter size and M* as low as few TeV !!
Dbrane models and XDType I Sring Theory framework
Brane world.Our Universe could be described as a hypersurface extended in p spatial dimensions:a pbrane
R >> r >> ℓP
Matter would be trapped to the brane, whereas gravity propagates on all 4+n dimensions
Bottomup: To study of these models we can use an effective field theory description with M* as the UVcutoff.
Dpbrane
3brane
Open String
Closed String
( Gravity )
r
(Gauge)
R
Perperdicular XD
Dbrane models and XDType I Sring Theory framework
Bottomup: To study of these models we can use an effective field theory description with M* as the UVcutoff.
If Einstein gravity theory holds, fundamental gravity coupling does not necessarily coincide with the Newton constant!!
The simplest scenario would be considering a flat topology for the extra space, where the bulk is a factorized manifold of the form M4×T n
ADD, 1998
M* ≈ few TeV ?!!
Notice:Vn encodes the actual geometry of the internal manifold.
3brane
r
4 brane
Large and short XDA simple toy model one can consider is an effective field theory on a the torus topology.
R >> r ≥ M*−1
as S is dimensionless:
 πR
0
πR
zero mode
KK modes
Dimensional reduction: 5D toy modelConsider a bulk scalar field φ(x; y).φ(x; y) = φ(x; y + 2R)
Thus, φ(x; y) can be Fourier expanded
After inserting in the bulk action:
for A=,5
we get the effective action:
where the KK mass:
Expected from PAPA = p p + p52= m2
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Dimensional reduction: 5D toy modelOn the Torus Tn the spectrum would be similar, but degeneracy on KK levels increases.
 πR
0
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πR
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πR
U(1)/Z2
cos(ny/R)
sin(ny/R)
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n=3
n=2
n=1
odd modes
even modes
n=0
Dimensional reduction: the S1/Z2 orbifoldTake the circle and identify opposite points on it.
Z2 : y → y
To get a feeling for the phenomenology, consider:
Using the KK expansion, we get:
One gets asuppressed effective coupling:
Production of a bulk mode out of brane collisions:
Decay rates:
since N = MR = MP2 / M*2
k
k ± p
Bulk to Bulk Coupling SuppressionTake for instance the coupling in 5D on [ πR, πR ]
Integrating over the extra dimension we shall get
Orthogonality implies
Fifth momentum is “conserved” in a way that does not constrain the actual direction of the transverse component( the sign of p5 is “irrelevant”)
Actually, former p5 conservation is now manifested only as a parity: (1 )KK
We’ll come back to the orbifold latter…
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MN
MN
MN
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n
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M
*
The GravitonGiudice, Ratazzi & Wells, NPB 544,3 (1999)
Han, Lykken & Zhang, PRD 59, 105006 (1999)
Take the action for a particle on the brane
and consider the perturbed metric
hMNis a symmetric tensor, + general coordinates invariance of GR, implies: D(D  3)/2 independent deg. of freedom
we get, at first order in h the Matter to graviton effective coupling
Possible physical processes are:
i) Graviton exchange
ii) Graviton emission
where
At the classical limit Graviton exchange should provide the law for Gravitational interactions
Existence of extra dimensions could be probed by short distance gravity experiments
At large distances, gravity would appear as effectively four dimensional:
At short distances, however, it would
reveal its higher dimensional nature
Both regimes do match :
At intermediate scales, just above threshold:
But,… How large could R be?...
r2
C.D. Hoyle et al., hepph/0405262
a
r ≥ a
Sensible to 10–16 N·m
Simplest Bounds on M* and RTesting Newton’s law at short distances is not that easy …
F~ GNr1 r2 a4
For: r ~ 20 gr/cm3:
F ~ 10–5 N × ( a/10 cm )4
This was indeed the strength measured by Cavendish in 1798 !!
Going to smaller distances must face:
– Surface electrostatic potentials:~ r −2
– Magnetic forces~ r −4
– Casimir forces, important for r ~ m
Experiments probing short distance gravity have tested Newton’s law down to 160 m.No deviations had been found.
EötWas experiment (Washington)
C.D. Hoyle et al.,hepph/0405262
Testing for:
where, for extra dimensions (r ≥ R )
α= 8n/3

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R
Simplest Bounds on M* and RConsider
For n=1:

³
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R
Simplest Bounds on M* and RConsider
For n=2:
A solution to the Hierarchy Problem?
Might such a low fundamental scale be possible?
Feynman diagrams for
During a collision of center mass energy√s there are about accesible KK graviton modes!!
Graviton phenomenology and boundsSome Processes:Main signal would be energy loss by gravitational radiation into the bulk by any physical process on the world brane
Giudice, Ratazzi & Wells, NPB 544,3 (1999)
Han, Lykken & Zhang, PRD 59, 105006 (1999)
Each mode has Planck suppressed couplings
Thus:
Feynman diagrams for
Graviton phenomenology and boundsGiudice, Rattazzi, Wells (1999); Mirabelli, Perelstein, Peskin (1999); Han, Likken, Zhang (1999); Cheung, Keung (1999); Balázs et al., (1999); Hewet (1999)…
LHC:
Missing energy due to graviton emission atLHC, as a function of M*, in a monojet production
Graviton phenomenology and boundsGiudice, Rattazzi, Wells (1999)
unpolarized beams background limit
Total cross section forγ + gKKproduction ate+ e linear colliderat 1 TeV center mass energy.
Giudice, Rattazzi, Wells (1999)
Abazov, et al., DØ Collab. 2003
95% C.L. exclusion contours on M* and number of extra dimensions (n) for monojet production at DØ (solid lines).
Dashed curves correspond to limits from LEP, and the dotted curve is the limit from CDF, both for γ + gKK production
Explicit computations of graviton emission leads to some bounds:
Giudice & Strumia, 2003
95% CL limits on M* (in TeV) for n extra dimensions from graviton emission processes in differente experiments
Graviton phenomenology and boundsLHC:
Giudice & Strumia, 2003
Graviton phenomenology and boundsGiudice, Ratazzi & Wells, NPB 544,3 (1999)
Han, Lykken & Zhang, PRD 59, 105006 (1999)
Bin integrated lepton pair invariant mass distribution for DrellYang production for M*=2.5 and 4.0 TeV at LHC
95 % C.L. search reach for M* as a function of the integrated luminosity at LHC
Graviton phenomenology and boundsJ.L. Hewett, 1999
Bin integrated angular distribution (z=cos θ) for e+ e → +  and M*=1.5 TeV
Graviton phenomenology and bounds95 % C.L. search reach for M* as a function of the integrated luminosity at e+ e colliders
J.L. Hewett, 1999
n
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Cosmological bounds
M* 10 TeV; n=2 Tr < 100 MeV
Hannestad & Raffelt PRD 64 (2001); PRL 88 (2002)
These bounds:
gkk→ gKK + gKK
Mohapatra, Nussinov & PérezLorenzana, PRD 68 (2003)
Microscopic Black Hole production
S.B. Giddings, S. Thomas, PRL 65 (2002) 056010
S. Dimopoulos, G. Landsberg, PRL 87 (2001) 161602
If M* ~ TeV, we may be exploring effects of Quantum Gravity in LHC/ILC
In (4+n)D Schwarzschild radious:
If impact parameter in a collision is smaller than rS, a BH will form MBH = √s
Cross section:
About 107 BH’s per year LHC !!! (?).
Rapid evaporation:
A. Mücka, A. Pilaftsis, & R. Rückl,hepph/0312186