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Extra Dimensional Models

Monday Seminar. EPFL, the 25 th of June 07. Extra Dimensional Models. Géraldine Conti. Picture from Scientific American. Monday Seminar. Géraldine Conti. EPFL, the 25 th of June 2007. Outline. The Standard Model (SM) limits : Conceptual Problems

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Extra Dimensional Models

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

  2. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Outline • The Standard Model (SM) limits : • Conceptual Problems • Experimental clues for New Physics • Avenues beyond SM : • Supersymmetry (SUSY) • Technicolor • Little Higgs • Extra Dimensions (ED) • …

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

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

  5. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Experimental clues for New Physics (2) • Muon g-2 : 3.3 deviation in the  anomaly (a)  New physics : Light SUSY ? • Precise sin2Wmeasurements do not match:  New physics in Zbb vertex ? Davier,Hocker, hep-ph/0701163v2 (2007)

  6. SM t H H SUSY MGUT t MPl Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Solutions to the SM Problems… Problems new Models Jungman, Kamionkowski, Griest, Phys. Rept. 267 (1996) 195-373 Hagelin, Kelley, hep-ph/9211210 (1992) Joseph Lykken, Fermilab, SSI 2004 Kainulainen, Tuominen, Virkajärvi, Phys. Rev D75 (2007) 085003 Birkedal, Noble, Perelstein, Spray, Phys.Rev. D74(2006) 035002

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

  8. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 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, 1165-1172

  9. Flat ED : ADD Model (1) R r bulk brane (y=0) Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 • SM fields are localised on a (3+1)-D subspace (brane) which can havea 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 gravity R = compactification radius  = number of ED =1 : R=8*1012m =2 : R=0.7mm =3 : R=3nm =4 : R=6*10-12m

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

  11. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Tests on Newton’s law (3) Hoyle and al., Phys. Rev. D70, 042004 (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, 1165-1172 Hoyle and al., Phys. Rev. D70, 042004

  12. At LEP2 : • e+e- tt Limits on MD : MD > 1TeV • e+e-ss Bernardi, LPNHE, CHEP-2002 Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Search for ADD signals at LHC (4) Signature : jet + large missing ET At LEP2 : • Direct Search : KK Excitations of gravitons • Indirect Search : Virtual exchange e+e-  /ZGKK Limits on R : R<0.26mm (=2) R<13pm (=4) R<6 10-12m (=6) (ATL-PHYS-2000-016) Bernardi, LPNHE, CHEP-2002 Signature : deviations on the cross-sections  from SM (ATL-PHYS-2001-012)

  13. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 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 expected10-33-10-34 luminosity, several BH/min! Decay signature : ~6 particles for each decay, emitted spherically (via Hawking radiation) MPl=1TeV, =2

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

  15. KK excitations of gravitons (radions) Spin-2 resonances production (gravitons) pp (gg or qq)  GKK  e+e- M1=1.5 TeV G1 G2 G3 Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Search for RS signals at LHC (2) M=1.5 TeV 100fb-1 (JHEP 09 (2000) 019 – ATL-PHYS-2000-029) Low branching ratio (BR=2%), but clear signal in the ECAL of ATLAS. (ATL-PHYS-2000-029) * is the angle between the decay e- and the beam direction in the dilepton CM frame

  16. MD~ few TeV to solve it Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Solutions to the SM problems • Hierarchy Problem : • 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

  17. « Beyond Standard Model » Examination Géraldine Conti CERN, the 24th of May 2007 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 http://www-d0.fnal.gov/Run2Physics/WWW/results/final/TOP/T05D/T05D_files/aq_particle_mass_small.gif

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

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

  20. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Back-up : Dark Energy/Matter Dark Energy : 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 1998 1A supernova Dark Matter : Virial theorem : Brightness  Distance Kinetic Energy -0.5*Potential Energy Redshift  Scale factor

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

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

  23. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 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 runlogarithmically • Disfavoured by LEP and Tevatron (top quark mass,…)

  24. Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 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~1TeVinclude 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,…)

  25. MPl Monday Seminar Géraldine Conti EPFL, the 25th of June 2007 Back-Up : SUSY • Boson-fermion symmetry  equal number of degrees of freedom • R-parityconservation  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)

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