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2014 : extra dimensions centennial from the Standard Model to extra dimensions

2014 : extra dimensions centennial from the Standard Model to extra dimensions many “flavors” of extra dimensions direct and indirect effects of extra dimensions at the TeV scale current results and upcoming discoveries. :. Gunnar Nordstrom

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2014 : extra dimensions centennial from the Standard Model to extra dimensions

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  1. 2014 : extra dimensions centennial • from the Standard Model to extra dimensions • many “flavors” of extra dimensions • direct and indirect effects of extra dimensions at the TeV scale • current results and upcoming discoveries

  2. : Gunnar Nordstrom Uber die Moglichkeit das electromagnetiche Feld und das Gravitationsfeld zu vereiningen Phys. Z. 15, 504 1914 : : Abstract. It is shown that a unified treatment of the electromagnetic and gravitational fields is possible if one views the four dimensional space time as a surface in a five dimensional world

  3. Thedor Kaluza Oscar Klein Kaluza Th.Sitzungsber. Press.Akad.Wiss.Math K1 (1921) 966 Klein O. Z.Phys. 37 (1926) 895

  4. Kaluza and Klein started from 5-dim gravity and derived 4-dim gravity plus electromagnetism They compactified the 5th dimension around a circle of radius R (“cylinder condition”) 5 GN=1/(MP)2 4

  5. the Standard Model • a list of particles with their “quantum numbers”, • about 20 numbers that specify the strength of the various particle interactions, • a mathematical formula that you could write on a napkin. 20s

  6. 32? 7? extra dimensions? 6? Experimentscan actually discover them! String theory demands extra dimensions. 20sec

  7. 16 orders of magnitude puzzle hierarchy of scales 10-17 cm Electroweak scale range of weak force mass is generated (W,Z) strong, weak, electromagnetic forces have comparable strengths 10-33 cm Planck scale GN ~lPl2 =1/(MPl)2 1028 cm Hubble scale size of universe lu 1m

  8. signals from extra dimensions in short range gravity observations • in particle collision observations in astrophysical/cosmological observations how do we see a hidden dimension? • what particles can move in that dimension • how big is that dimension • what is its shape

  9. Frameworks • ADD type of models: the extra dimension(s) are finite (i.e. compactified), the world is a “braneworld”, gravity (or SM singlets) propagate in the bulk. Hierarchy is generated by a large volume of the extra dimensions. • Direct emission/virtual exchange. • RS type of models: the extra dimension(s) are infinite. Hierarchy is generated from a strong curvature of the extra dimensional space. • Direct resonant production of the spin-2 states in the graviton KK tower. • Universal (Yale) type of models : No branes. Momentum conservation; Pair production of KK excitations.

  10. Nima Arkani-Hamed Savas Dimopoulos Gia Dvali hiding the extra dimensions (I) compactification 1m

  11. Gauss’s Law If the n extra dimensions are compactified down to sizes R, then Gauss’s Law 1m

  12. 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: KK momentum tower of states (n is the mode number, for 2 extra dimensions two modes etc…) p 0

  13. Pick the effective (higher dimensional) Planck Scale at 1TeV, then

  14. hiding the extra dimensions (II) brane-worlds There could be other branes which would look like dark matter to us Standard Model particles are trapped on a brane and can’t move in the extra dimensions

  15. Infinite Randall - Sundrum Our world brane G Mother brane 5th dimension Zero mode graviton is trapped on the mother brane (Planck brane)

  16. it gets stronger at lower energies if there are extra dimensions…. (4+n)d gravity gravity gets stronger at extremely high energies (or short distances). 4d gravity force strength energy

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

  18. melectronmelectron r2 F=GN melectron melectron r gravitons are the most robust probe of extra dimensions gravity is so weak that we have never even seen a graviton. The gravitational attraction between two electrons is about 1042 times smallerthan the electromagnetic repulsion.

  19. graviton production in collider experiments: graviton emission • Each KK-graviton state couples to the wall with Planck supressed strength • The number of KK-states ~(ER)d • The sum over all KK-states is not MPl supressed but MPl(4+d) supressed i.e. MEWK supressed so we have sizable cross sections graviton Exchange Fermion or VB pairs at hadron or e+e- colliders

  20. Collider Detector at Fermilab

  21. graviton emission in particle collisions www.columbia.edu/~lab71

  22. graviton emission simulation:

  23. concentric cylindrical layers energy deposited from the particle debris of the collision in the middle

  24. “lego” event display

  25. Two events are graviton simulation and one is real CDF data: Can you pick the gravitons?

  26. two events are real CDF data and one is graviton simulation; Can you pick the graviton?

  27. qqbar->g G (d=2, M=1TeV, s=1.8TeV) [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] Lykken/Matchev/Burkett/Spiropulu

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

  29. qq  Gg [Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)] very very optimistic estimates n MSreach,Run I MS reach, Run II 2 1100 GeV 1400 GeV 3 950 GeV 1150 GeV 4 850 GeV 1000 GeV 5 700 GeV 900 GeV LHC 100fb-1 8.5 TeV 6.8 TeV 5.8 TeV 5.0 TeV

  30. Monojet+missing energy: DØ limit

  31. Monojet+missing energy: CDF Expected number of gravitons for 84pb-1 Result very soon

  32. e+e- gG@L3 [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and cor. version: hep ph/9811291] (GMSB analyses)

  33. e+e-GZ ( a la Higgs analyses) [Balazs, Dicus, He, Repko, Yuan, hep-ph/9904220, Z width] [Cheung, Keung, hep-ph/9903294, recoil mass] MET+jets n sZG(pb) e sZG95%(pb) Ms(TeV) 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 L3: Phys. Lett. B470, 281 (1999) Visible Mass analysis ALEPH-CONF-99-027 Total cross section analysis

  34. Monojet + missing energy: LHC reach Ian Hinchliffe

  35. Pair production via virtual graviton exchange 2 e.g > Gravity effects interfere with SM effects > 3 terms in the production cross section: SM, intrerference, gravity > the sum over the KK states is divergent and a cutoff is required (Ms)

  36. Virtual exchange: dielectron and diphoton D0 limits

  37. M(gg) = 574 GeV cosq* = 0.86

  38. Virtual exchange: diphoton CDF analysis

  39. (anomalous Zgg couplings analyses,WW x-section,Zg) Standard Model e+e-gg,VV Interference Term Gravity Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] Agashe, Deshpande, Phys. Lett. B456, 60 (1999)

  40. Two-photon measurements at LEP-II

  41. Summary LEP 184 GeV 189 GeV Graviton Emission 202 GeV e+e- gG e+e- ZG n=2 n=3 n=4 n=5 n=6 n=2 n=3 n=4 n=5 n=6 1.28 0.97 0.78 0.66 0.57 0.35 0.22 0.17 0.14 0.12 A D L3 1.38 1.02 0.84 0.68 0.58 1.02 0.81 0.67 0.58 0.51 0.60 0.38 0.29 0.24 0.21 Virtual Graviton Exchange e+e- m+m- t+t- qq f f gg WW ZZ Combined ALL 0.80 1.03 0.63 0.68 0.57 0.59 0.66/0.61 0.55/0.55 (bb) 0.82 1.04 0.91 0.92 0.84/1.12 (<189) 0.75/1.00 A D L3 O 0.59 0.73 0.56 0.65 0.60 0.76 0.69 0.71 0.60/0.76 (ff) (<202) 0.91 0.99 0.56 0.69 0.58 0.54 0.49 0.49 0.84 1.00 0.80 0.79 0.68 0.79 0.76 0.77 0.87/1.07 (<189) 0.82/0.89 (VV) 0.63 0.60 0.50 0.63 0.61 0.68 0.63 0.64 0.61/0.68 (ff) (<189)

  42. RS phenomenology 1500 GeV KK graviton/ its tower of states at LHC e+e-m+m- 500 GeV KK graviton/ its tower of states at a lepton collider 500 GeV KK graviton and neutral gauge boson excitations Davoudiasl, Hewett,Rizzo

  43. A spin 2 graviton: Can we tell? 1.5 TeV graviton in Randal Sundrum at LHC

  44. Linear Collider (?,~2012) Large Hadron Collider (CERN, 2006) new accelerators for new physics

  45. Plethora of new models that involve extra dimensions Use Extra Dimensions Geomerty to solve: EWKB hierarchy problem SUSY Breaking flavor Breaking neutrino masses proton decay supression Grand Unification the cosmological problem More ideas are being explored

  46. hiding the extra dimensions (III) no need to hide them extra-new ideas (Arkani-Hamed et al, Hill et al…..) Deconstructing dimensions and sting theories: The extra dimension(s) emerges from the theory, is well used, and then the theory comes back to the normal 4 dimensions serviced and healthy and with all the necessary Higgses. No tricks.

  47. what is the physics that connects the gravitational scale and the scale of the typical mass of the elementary particles • what are the dimensions and dynamics behind spacetime • how is string theory connected to the world

  48. Space and time may be doomed.E. Witten I am almost certain that space and time are illusions. N. Seiberg The notion of space-time is clearly something we’re going to have to give up.A. Strominger If you ask questions about what happened at very early times, and you compute the answer, the answer is: Time doesn’t mean anything. S. Coleman

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