2. MARIA SPIROPULU MARCH 30 2000 Vanderbilt University Physics & Astronomy Colloquium Experimental Clues From Higher Dimensions

3. Outline  Extra Old : 7Variations on a theme: Embedding the 3+1 spacetime to a higher dimensional structure 7Table-top experiments: Status 7 Collider experiments: Results and prospects

4. the 5th dimension is 75 Years Old Kaluza and Klein started from 5-dim Einstein gravity and derived 4-dim gravity plus electromagnetism The 5th dimension is compactified around a circle of radius R

5. Compactification around a circle of radius R e.g. For many extra dimensions BUT in the KK case the compactification radius is too very small.

6. String theory and Extra dimensions String Theory, or M-theory implies the existence of 7 extra spatial dimensions which must be compact since we do not see them. Many possible physical scales of string theory : M s ~10 16 GeV ; 1/R ~ 10 16 GeV 1 M s ~10 11 GeV ; 1/R ~ 10 9 GeV 1 M s ~ 10 4 GeV ; 1/R ~ 10 3 GeV 1 M s < 10 3 GeV ; 1/R ~ meV 1

8. Kaluza-Klein modes If a spatial dimension is periodic then the momentum in that dimension is quantized: From our dimensions of view the KK modes get mass: p 0 KK momentum tower of states

9. Gauss’s Law If the δ extra dimensions are compactifid down to sizes R, then Gauss’s Law The Planck Scale from our dimension of view, 10 19 GeV 4+  Planck Scale M s M D M * … any scale that in the higher dimensional theory is taken O(TeV)

10. The size of the extra dimension No way Explore in sub-mm gravitational experiments/collider... M-theory limits Set the higher dimesional Planck scale to m EWK, the Planck scale to 10 19 GeV then

11. The extra world picture The SM is confined on a 4d wall Gravity exists in a 4+d “bulk” Gravity feels week on the wall because of the enormity of the bulk volume Each KK-graviton state couples to the wall with Planck supressed strength The number of KK-states ~(ER)  The sum over all KK-states is not M Pl supressed but M Pl(4+  ) supressed i.e. M EWK supressed so we have sizable cross sections

12. Variations on a theme many large toroidal extra dimensions (Arkani Hamed-Dimopoulos-Dvali) one infinite extra dimension (Randall-Sundrum) one infinite extra dimension for us, and the Planck brane for gravity (Randall-Lykken) longitudinal extra dimensions in the TeV range (Antoniadis-Benakli-Quiros) and more...

13. Variations on a theme Weak-10 3 Planck What (kind of like a U duality) is going on??? Energy Desert Space Oasis 10 19

14. Experimental (Low Scale) Quantum Gravity KK excitations of gravitons in the bulk neutrinos in the bulk gauge bosons in the bulk Deviations from Newton’s law at the mm range Astrophysics-cosmology constraints

15. Torsion Balance : Could Archimedes’ have measured G N 19 Centuries before Newton’s Principia

16. Cavendish Type Setups

17. Table -Tops Add a Yukawa term to the Gravitational Potential

18. Table Tops hep-ph/9805217 Long,Chan,Price 1KHz 100u

19. Table Tops Goal: Measure gravity to 1% at distances of 100 

20. MI Tevatron D0  CDF  Collider searches for Extra Dimensions Protons run the 4 mile ring about 50000/sec CERN,European Center for Nuclear Research

21. Particle Detecting tracker Muon chambers calorimeters

22. The Particles and Their Interactions up down charm strange top bottom electron neutrino muon muon neutrino tau tau neutrino forces & carriers quarks & leptons Strong Electromagnetic Weak Gravity Gluon photon W,Z graviton Relative Strength Today 1 10 -3 10 -14 10 -42

23. Grand Unification Force Strength Higher Energy electromagnetic strong weak gravity new

24. The scale of experimental particle physics Number of researchers For discovery of

25. Direct Graviton Emission at electron positron collisions As no statistically significant signal is observed, 95% Confidence Limits are placed on the fundamental mass scale M D, as a function of the number of extra dimensions

26. e+e-  G 

27. e+e-  G  2 0.64 0.56 0.29 0.60 3 0.08 0.56 0.30 0.38 4 0.01 0.55 0.30 0.29 n  ZG (pb)   ZG 95% (pb) Ms(TeV) MET+jets

28. e+e-  >  Standard Model Interference Term Gravity

29. Two-photon measurements at LEP-II 161-189GeV  T (+)>987 GeV (189:>890 GeV)  T (-)>866 GeV (189:>770 GeV) 192-202 GeV

30. Two-photon measurements at LEP-II M S >615 GeV/c 2 ( =+1) M s >703 GeV/c 2 ( =-1)

31. Two-photon measurements at LEP-II

32. e + e -  > ff For ff other than ee the integrated interference term for scattering angles from 0 to  is ZERO. The interference between graviton and t-channel SM Bhabha is giving sizable contributions  good sensitivity Terms ~cos 3 , ~cos 4  make differential cross sections a unique signature Giudice,Rattazi,Wells/Hewett/Rizzo

33. Bhabha scattering results M S >810 GeV ( =+1) M s >720 GeV ( = -1)

34. Bhabha scattering results M S >920 GeV ( =+1) M s >710 GeV ( =-1) ALEPH,OPAL,DELPHI,L3 combined: (Bourilkov hep-ph/9907380) M S >1.26 TeV ( =+1) M s >960 TeV ( =-1)

35. e + e -  > ff     M S >580 GeV ( =+1) M s >510 GeV ( =-1)     M S >450 GeV ( =+1) M s >550 GeV ( =-1)

36. e + e -  > WW, ZZ T.Han, J.D.Lykken, R.-J.Zhang hep-ph 9811350 K.Agashe, N.G.Deshpande hep-ph 9902263 W + W - M S >650 GeV ( =+1) M s >520 GeV ( =-1) ZZ M S >470 GeV ( =+1) M s >460 GeV ( =-1)

37. LEP summary Virtual Graviton Exchange Limits on Ultraviolet Cutoff Scale (TeV) Real Graviton Production Limits On Extra Dimensions  G,ZG ~1 TeV to ~500 GeV for n=2 to n=6

38. Tevatron (virtual) Landsberg,Cheung hep-ph/9909218 Drell-Yan and diphoton production with virtual graviton exchange

39. The Three Components

40. Tevatron (direct) Only qqbar->g G (PYTHIA 6.115 + graviton process),  =2, M=1TeV,  s=1.8TeV Lykken/Matchev/Burkett/Spiropulu

41. qq->Gg

42. Case  =6 Only qqbar->g G (PYTHIA 6.115 + graviton process),  =6, M=1TeV,  s=1.8TeV

43. RUNII Display Only qqbar->g G (PYTHIA 6.115 + graviton process),  =6, M=1TeV,  s=2TeV, GEANT CDF preliminary RUNII simulation and display

44. Outlook 8 Sub-mm gravity experiments are expected to announce results very soon (maybe APR00) 8More Collider results and projections on the way 8LHC and (?) LC will probe effective higher dimensional Planck scales up to many (tens of) TeV 8Very important cosmological constraints and implications 8More extra dimensions model building (infinite extra dimensions, trap gravity on the Planck brane, string phenomenology &tc)

45. Extra Dimensions Stats

46. Neutrinos in the bulk Dimopulos, Hamed,Dvali Russel, hep-ph/9811448 Martin,Wells hep-ph/9903259 If the R lives in the extra dimensions as a KK tower of states and the Dirac neutrino masses arise from y H R L so that m =y u where u is the Higgs vev 175 GeV then the decay of the Higgs to L R (i) is proportional to the small y 2, but also to the sum of the KK states (all  with m<m H ) (m H R) .

47. Z*H(invisible) For some reasonable values, m H =100GeV, d=3, m 2 ~10 -6 eV 2 and M D =1 TeV the above ratio is > 100 … l+ l- Signal l+ l- Background: Z(ll)Z( ) WW,top,mismeasurements.. P T (l)>12 GeV, |  |<2 |m ll -m Z |<7 GeV no jet with Et>10 GeV

48. Z*H(invisible)

49. m H (GeV)

50. Strings again A lot of work in string phenomenology domain with large extra dimensions The dominant new physics effects may come from stringy physics Look for string resonances and other form factor corrections to SM 2-body reactions Impressive sensitivity of LHC,LC

51. Gauge Bosons in the Bulk Antoniadis,Quiros,Benakli hep-ph/9905311 Rizzo,Wells hep-ph9906234 One motivation is the weak scale SUSY breaking.The compactification scale of the extra dimension(s) considered in these scenarios is of the order of the SUSY breaking scale taken to be of the order of the EWK scale. quarks and leptons are confined on a 4d boundary gauge fields live in the 5d bulk The gauge boson KK states have an additional  2 strength in their interactions

52. implications The vector boson KK modes have masses From precision EWK measurements R -1 ~3.5 TeV Z (n),  (n) Also limits from: PEW:LEP,SLD,NuTeV..,had:direct KK gauge boson,e+e-:deviations in final state fermion observables

53. NLC

54. String Resonances Accomando,Antoniadis,Benakli hep-ph/9912287 Production of a gluon excitation at the LHC(  s=14Te, L=100fb -1 ) (also with dijet excess TeVII,20fb-1, Rc=4 TeV) l W KK excitations at LHC

55. Stringy Model Building&Searches http://itp.ucsb.edu/online/susy_c99/peskin/ 1000 GeV LC projections M>8 TeV (Ms>2.7 TeV M H >5.4 TeV) 183 GeV ALEPH data M>1200 GeV (Ms>400 GeV M H >810 GeV) M H =Hewett’s ultraviolet cutoff