extra dimensional models

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Extra Dimensional Models

Géraldine Conti

Monday Seminar

EPFL, the 25th of June 07

Picture from Scientific American

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are needed to see this picture.Outline

• The Standard Model (SM) limits : – Conceptual Problems– Experimental clues for New Physics

• Avenues beyond SM : – Supersymmetry (SUSY)– Technicolor– Little Higgs– Extra Dimensions (ED)– …

Géraldine Conti EPFL, the 25th of June 2007Monday Seminar

QuickTime™ and aTIFF (Uncompressed) decompressor


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are needed to see this picture.The SM conceptual problems

• Conceptual problems of the SM : – The “Big” Hierarchy Problem

– The Little Hierarchy Problem (low energy) • The Higgs mass mh diverges in the SM because of radiative corrections mh:

For the top-loop : Should be small ~ O(1TeV)


mW MGUT MPl

1(M)

2(M)

3(M)

logM

102GeV 1016GeV 1019GeV

SM Low Energy effective theory

Quantum Gravity

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are needed to see this picture.Experimental clues for New Physics (1)

• Experimental Clues :– Dark Energy (73%).

– Dark Matter (23%).

– Flavour problem

– Baryogenesis

– Neutrinos masses,…

In the Universe :


X-ray emission of the hot gas Gravitational Lensing

Collision between two clusters of galaxies :

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are needed to see this picture.Experimental clues for New Physics (2)

– Muon g-2 : 3.3 deviation in the anomaly (a)

New physics : Light SUSY ?

– Precise sin2W measurements do not match:

New physics in Zbb vertex ?

Davier,Hocker, hep-ph/0701163v2 (2007)


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are needed to see this picture.Solutions to the SM Problems…

SUSY Divergences cancelled between superpartners (top - stop loops)

Neutralinos (Lightest (R-parity) stable particle)

Technicolor

Fermion masses are protected (no fundamental scalars (0-spin))

Massive 4th family neutrino

Little Higgs

Divergences cancelled between fields of the same spin (fermions cancel fermions…)

Heavy photon (Lightest T-parity odd stable particle)

H H

t

t

MGUT

MPl

SM

SUSY

Kainulainen, Tuominen, Virkajärvi, Phys. Rev D75 (2007) 085003

Jungman, Kamionkowski, Griest, Phys. Rept. 267 (1996) 195-373

Hagelin, Kelley, hep-ph/9211210 (1992)

Modelsnew

Problems

Birkedal, Noble, Perelstein, Spray,

Phys.Rev. D74(2006) 035002http://physicsweb.org/articles/world/15/11/ 3

Joseph Lykken, Fermilab, SSI 2004

http://physicsweb.org/articles/world/15/11/ 3


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are needed to see this picture.Extra Dimensions : Introduction

• The idea of Extra Dimensions (ED) comes from the beginning of the 20th Century, with Nordström (1914), Kaluza (1925) and Klein (1926) (unification of gravity and electromagnetism in a 5D theory). The ED are already present in String theory (10D).

• Fundamental Planck scale brought down to ~ 1TeV.• Notations :

MPL = effective (4D) Planck mass (1019GeV)

MD = fundamental ((4+n)D) Planck massR = compactification radius


Forces Relative strength

Gravitation 1

Weak 1025

EM 1036

Strong 1038

GN~1/M2Pl

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are needed to see this picture.Different ED Models

1) Gravity in Flat ED : Arkani-Hamed, Dimopoulos, Dvali (ADD) Model

2) Gravity in Warped ED :

Randall-Sundrum (RS) Model

3) SM Fields in Waped ED

Giudice, Journal of Physics G, 2006, 1165-1172


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• SM fields are localised on a (3+1)-D subspace (brane) which can have a thickness r.

• Weakness of gravity : Gravitons can propagate in the whole bulk

• Effective 4D Plank mass is given by :

• For MD=1TeV :

MD = fundamental scale of gravityR = compactification radius

R

r

bulk

bra

ne

(y=

0)

=1 : R=8*1012m =2 : R=0.7mm =3 : R=3nm =4 : R=6*10-12m

Flat ED : ADD Model (1)

= number of ED


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• Particles in the ED : D-dimensional bosonic fields

Discrete because of finite size of compactified space

(n) = nth Kaluza-Klein (KK) excitations of corresponding to particles (GKK gravitons) propagating in 4D with masses:

States spaced in masses : Tower of KK modes

Flat ED : ADD Model (2)


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Tests on Newton’s law (3)

• Searches for deviations from the gravitational law, parameterized by a modified newtonian potential :

Hoyle and al., Phys. Rev. D70, 042004 (2004)

Experimental limits on and :

R < 130m at 95% CL MD > 1.9TeV for =2

• For =2, Newton’s law verifiedup to distances~130m :

Hoyle and al., Phys. Rev. D70, 042004Giudice, Journal of Physics G, 2006, 1165-1172

(), (R)


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are needed to see this picture.Search for ADD signals at LHC (4)

• Direct Search : KK Excitations of gravitons

• Indirect Search : Virtual exchange



Signature : deviations on the cross-sections from SM

Signature : jet + large missing ET

(ATL-PHYS-2000-016)

(ATL-PHYS-2001-012)

Limits on R :R<0.26mm (=2)

At LEP2 : e+e- /ZGKK

R<13pm (=4)R<6 10-12m (=6)

Bernardi, LPNHE, CHEP-2002

e+e- tt

MD > 1TeV

At LEP2 :

e+e- ss

Limits on MD :

Bernardi, LPNHE, CHEP-2002


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are needed to see this picture.Search for Black Holes (5)

Schwarzschild radius Rs for a colliding system in D=4+

BH production cross section with MBH>MD=1TeV :

Experimental requirements for BH production :


MP

l=1

Te

V, =

2

1) √S > MD 2) Impact parameter b<RS

=15pb=1.5·10-35cm-2 at expected10-33-10-34 luminosity, several BH/min!

Decay signature :

~6 particles for each decay, emitted spherically (via Hawking radiation)

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are needed to see this picture.RS Model (1)

• Weakness of gravity due to the Warp factor.• 4D masses m4 scaled down :

• GKK excitations masses (at LHC (ie on the TeV brane) ) :

The metric solution of Einstein equations is here :

Two free parameters : M1 and c, with

y = ED coordinatek = ADS curvature

bulk SM

particle

Planck

y=0

y=R

Warp factor :

IR brane

UV brane


xn=3.8, 7, 10.2,…J1(xn)=0

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are needed to see this picture.Search for RS signals at LHC (2)

• KK excitations of gravitons (radions)

• Spin-2 resonances production (gravitons)

(JHEP 09 (2000) 019 – ATL-PHYS-2000-029)M=1.5 TeV 100fb-1

Low branching ratio (BR=2%), but clear signal in the ECAL of ATLAS.



M1=1.5 TeV

G1

G2

G3

(AT

L-P

HY

S-2

000-

029)

pp (gg or qq) GKK e+e-

* is the angle between the decay e- and the beam direction in the dilepton CM frame


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are needed to see this picture.Solutions to the SM problems

Large compactified ED :

MDR should be large.

Small warped ED :

kR~12 is not too big.

MD ~ few TeV to solve it• Hierarchy Problem :

• Dark Matter Candidate: ?• Link to GUTs :

These ED models so far do not give links to GUT’s theories (all the SM particles are on the TeV brane )

Goldberger, Wise

Pomarol ; Agashe, Delgado, Sundrum


• Large corrections for EW precision tests

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are needed to see this picture.SM fields in Warped ED :

• SM particles propagate in a higher-dimensional space :

Géraldine Conti CERN, the 24th of May 2007« Beyond Standard Model » Examination

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http://www-d0.fnal.gov/Run2Physics/WWW/results/final/TOP/T05D/T05D_files/aq_particle_mass_small.gif

Explanation for the mass spectum of fermions & leptons

Gauge coupling unification at low scale is possible

Hierarchy problem still solved, because only the Higgs field is needed to be on the brane.

http://www-d0.fnal.gov/Run2Physics/WWW/results/final/TOP/T05D/T05D_files/aq_particle_mass_small.gif

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• Because of conceptual problems (hierarchy problem) and experimental clues (dark matter) at the weak scale, the SM must be extended.

• Several new interesting theories have emerged (SUSY, Technicolor, Little Higgs,…), but none of these has already been proved by experimental data.

• Among them, the Extra Dimensional Models offer interesting explanations to the problems cited above.

• ED theories are implicated in extensions of SUSY, Higgsless Models ((super)symmetry breaking) as well as in Grand Unification theories.

• The LHC will help us to select between the several existing models “Beyond the Standard Model”.

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are needed to see this picture.Back-up : GUTs

A direct extrapolation of the SM leads to GUTs (1016GeV).

The idea is that at high energies, all symmetries have the same gauge coupling strength (hypercharge Y, weak force L, quantum chromodynamics C).


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are needed to see this picture.Back-up : Dark Energy/Matter

Dark Energy :

Brightness DistanceRedshift Scale factor

Virial theorem :

Kinetic Energy -0.5*Potential Energy

It tends to increase the rate of expansion of the universe.

Study of the 1998 1A supernova

Its nature could be the cosmological constant (constant E density which fills the space homogeneously)

Dark Matter :


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are needed to see this picture.Back-up : g-2 experimenthttp://www.g-2.bnl.gov/physics/index.html

Spin magnetic moment :

g=Landé factor

From Dirac equation for the e- : g=2

Light SUSY :


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are needed to see this picture.Back-up : sin2eff


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are needed to see this picture.Back-Up : Technicolor

• All particles are fermions (except gauge bosons).

• The Higgs is a condensate of two fermions.

• New very strong binding force new ~103 QCD causes SU(2) x U(1) symmetry breaking.

E<new: the theory looks like the SM.

E>new: theory of fermions and masses run logarithmically

• Disfavoured by LEP and Tevatron (top quark mass,…)


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are needed to see this picture.Back-Up : Little Higgs ModelArkani-Hamed, Cohen and Georgi (2001)

• G (SU(2) x U(1))2 is a global symmetry group.

• H is pseudo-Goldstone boson coming from the G breaking at a TeV energy scale (to get a mass, it needs the breaking of 2 subgroups or 2 couplings)

• New particles with m~1TeV include fermionic partners for quarks and leptons, and also bosonic partners for gauge bosons.

• T parity conservation DM candidate• Problems with precision tests (can be fixed by

complicating the model : mirror fermions,…)


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are needed to see this picture.Back-Up : SUSY

• Boson-fermion symmetry equal number of degrees of freedom

• R-parity conservation Allows Lightest Stable Particle (LSP) to exist,…

• MSSM : – 2 Higgs doublets + 1 Scalar– More than 100 parameters– mh< 130GeV (as mh>114GeV, available parameter

space reduced)• mSUGRA (CMSSM):

– Flavour blind GUT constraints are added to reduce number of parameters (common mass for the scalar and common mass for the vectors) MPl


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are needed to see this picture.Back-Up : Newton law test

A molybdenum disc is suspended above an identical plate with a thin tungsten wire. Each disc has two rows of 21 carefully placed holes.

As the bottom disc rotates on a precision motor, the top disc reacts to the changing gravitational pull.


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