1. Extra Dimensional Models
Monday Seminar
EPFL, the 25th of June 07
Extra Dimensional Models
Géraldine Conti
Picture from Scientific American

2. Outline The Standard Model (SM) limits : Avenues beyond SM :
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 2007
Monday Seminar

3. 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:
102GeV
1016GeV
1019GeV
1(M)
2(M)
3(M) mW
logM
MGUT
MPl
SM Low Energy effective theory
Quantum Gravity
For the top-loop :
Should be small ~ O(1TeV)
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

4. Experimental clues for New Physics (1)
Dark Energy (73%).
Dark Matter (23%).
Flavour problem
Baryogenesis
Neutrinos masses,…
In the Universe :
Collision between two clusters of galaxies :
X-ray emission of the hot gas
Gravitational Lensing
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

5. Experimental clues for New Physics (2)
Muon g-2 : 3.3 deviation in the  anomaly (a)
 New physics : Light SUSY ?
Precise sin2W measurements do not match:
 New physics in Zbb vertex ?
Davier,Hocker, hep-ph/ v2 (2007)
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

6. 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)
Problems H t
MGUT
MPl SM
SUSY
new
Models
Jungman, Kamionkowski, Griest, Phys. Rept. 267 (1996)
Hagelin, Kelley, hep-ph/ (1992)
Joseph Lykken, Fermilab, SSI 2004
Kainulainen, Tuominen, Virkajärvi, Phys. Rev D75 (2007)
Birkedal, Noble, Perelstein, Spray,
Phys.Rev. D74(2006)
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

7. 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 mass
R = compactification radius
GN~1/M2Pl
Forces
Relative strength
Gravitation 1
Weak
1025 EM
1036
Strong
1038
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

8. Different ED Models
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,
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

9. Flat ED : ADD Model (1)
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 : R r
bulk
brane (y=0)
MD = fundamental scale of gravity
R = compactification radius
 = number of ED
=1 : R=8*1012m
=2 : R=0.7mm
=3 : R=3nm
=4 : R=6*10-12m
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

10. Flat ED : ADD Model (2)
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
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

11. Tests on Newton’s law (3)
Hoyle and al., Phys. Rev. D70, (2004)
Searches for deviations from the gravitational law, parameterized by a modified newtonian potential :
(), (R)
Experimental limits on  and  :
For =2, Newton’s law verified
up to distances~130m :
 R < 130m at 95% CL
 MD > 1.9TeV for =2
Giudice, Journal of Physics G, 2006,
Hoyle and al., Phys. Rev. D70,
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

12. Search for ADD signals at LHC (4)
Direct Search : KK Excitations of gravitons
Indirect Search : Virtual exchange
Signature : jet + large missing ET
At LEP2 :
e+e-  /ZGKK
Limits on R :
R<0.26mm (=2)
R<13pm (=4)
R< m (=6)
(ATL-PHYS )
Bernardi, LPNHE, CHEP-2002
Signature : deviations on the cross-sections  from SM
e+e-  tt
MD > 1TeV
At LEP2 :
e+e- ss
Limits on MD :
Bernardi, LPNHE, CHEP-2002
(ATL-PHYS )
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

13. Search for Black Holes (5)
Schwarzschild radius Rs for a colliding system in D=4+
Experimental requirements for BH production :
1) √S > MD
2) Impact parameter b<RS
BH production cross section with MBH>MD=1TeV :
=15pb=1.5·10-35cm-2  at expected luminosity,
several BH/min!
Decay signature :
~6 particles for each decay, emitted spherically (via Hawking radiation)
MPl=1TeV, =2
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

14. RS Model (1) The metric solution of Einstein equations is here :
y = ED coordinate
k = ADS curvature
bulk
SM particle
Planck
y=0
y=R
Warp factor :
Weakness of gravity due to the Warp factor.
4D masses m4 scaled down :
GKK excitations masses (at LHC (ie on the TeV brane) ) :
UV brane
J1(xn)=0
IR brane
xn=3.8, 7, 10.2,…
Two free parameters : M1 and c, with
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

15. Search for RS signals at LHC (2)
KK excitations of gravitons (radions)
Spin-2 resonances production (gravitons)
pp (gg or qq)  GKK  e+e-
M=1.5 TeV
100fb-1
(JHEP 09 (2000) 019 – ATL-PHYS )
Low branching ratio (BR=2%), but clear signal in the ECAL of ATLAS.
M1=1.5 TeV G1 G2 G3
(ATL-PHYS )
* is the angle between the decay e- and the beam direction in the dilepton CM frame
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

16. Solutions to the SM problems
Hierarchy Problem :
MD ~ few TeV to solve it
Large compactified ED :
 MDR should be large.
Small warped ED :
 kR~12 is not too big.
Goldberger, Wise
Dark Matter Candidate: ?
Link to GUTs :
Pomarol ; Agashe, Delgado, Sundrum
These ED models so far do not give links to GUT’s theories (all the SM particles are on the TeV brane )
Large corrections for EW precision tests
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

17. SM fields in Warped ED :
SM particles propagate in a higher-dimensional space :
 Gauge coupling unification at low scale is possible
 Hierarchy problem still solved, because only the Higgs field is needed to be on the brane.
 Explanation for the mass spectum of fermions & leptons
Géraldine Conti
CERN, the 24th of May 2007
« Beyond Standard Model » Examination

18. Conclusions
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”.
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

19. 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).
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

20. Back-up : Dark Energy/Matter
It tends to increase the rate of expansion of the universe.
Its nature could be the cosmological constant (constant E density which fills the space homogeneously)
Study of the A supernova
Dark Matter :
Virial theorem :
Brightness  Distance
Kinetic Energy
-0.5*Potential Energy
Redshift  Scale factor
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

21. Back-up : g-2 experiment
Spin magnetic moment :
g=Landé factor
Light SUSY :
From Dirac equation for the e- : g=2
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

22. Back-up : sin2eff Géraldine Conti EPFL, the 25th of June 2007
Monday Seminar

23. 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,…)
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

24. Back-Up : Little Higgs Model
Arkani-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,…)
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar

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

26. 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.
Géraldine Conti
EPFL, the 25th of June 2007
Monday Seminar