1. 1 mysteries of extra dimensions Joseph Lykken Fermi National Accelerator Laboratory

2. 2 a revolution in the making  the physics of extra dimensions is a revolution in the making  like the quantum mechanics revolution of the 1920’s, it is the result of many new ideas (from many people) coming together to give a radically new picture of physics and of the universe

3. 3 the universe: traditional view

4. 4 the universe: a bigger view extra dimensions of space the rest is terra incognita everything we know about is on this slice

5. 5  why do physicists think that there are extra dimensions of space?  what is the physics that hides extra dimensions?  how can experiments discover and explore extra dimensions? questions for this talk

6. 6 why do physicists think that there are extra dimensions of space? supermassive black hole in the center of galaxy M87 Reason #1: string theory particle physicists developed string theory to understand quantum gravity - to explain extreme physics such as goes on inside black holes

7. 7 string theory in string theory, all the elementary particles are merely different vibrations of a single substance called strings.

8. 8 string theory physicists have shown that quantum theory only allows one unique theory of quantum strings… but there is a catch: quantum strings need 9 spatial dimensions to wiggle in!

9. 9 why do physicists think that there are extra dimensions of space? Reason #2: mysteries of particle physics all ordinary matter is composed of just three kinds of elementary particles. but in particle accelerators we produce many more! why do these extra particles exist, and why these particles but not others?

10. 10 in string theory the answer lies in the shape of the extra dimensions determines how many ways the strings can vibrate, and thus whether there are 3, 12, or 137 kinds of elementary particles. particle physics data already in our hands may be an encrypted map of the geography of extra dimensions. slice of a 6 dimensional Calabi- Yau space

11. 11 why do physicists think that there are extra dimensions of space? Reason #3: the Big Bang the three spatial dimensions that we see are changing – expanding we don’t understand what is the dark energy driving the expansion today

12. 12 why do physicists think that there are extra dimensions of space? Reason #3: the Big Bang the three spatial dimensions that we see are changing – expanding we don’t understand what drove cosmic inflation in the early universe

13. 13 why do physicists think that there are extra dimensions of space? Reason #3: the Big Bang the three spatial dimensions that we see are changing – expanding we don’t understand what this was

14. 14 why do physicists think that there are extra dimensions of space? Reason #3: the Big Bang the three spatial dimensions that we see are changing – expanding extra dimensions may be the extra ingredient that explains the history of the universe

15. 15 if extra spatial dimensions exist, they must be (for some reason) difficult to probe physicists have uncovered several possible explanations: hidden dimensions e.g. the extra spatial dimensions are compact and small Nordstrom, Kaluza, and Klein, circa 1920

16. 16 compact extra dimensions what do we look for experimentally?…

17. 17 Kaluza-Klein modes if spatial dimension is compact then momentum in that dimension is quantized: from our point of view we see new massive particles! p 0 KK momentum tower of states

18. 18 how do we look for Kaluza-Klein particles?

19. 19 21 st century particle physics Fermilab’s Tevatron is the highest energy accelerator in the world today. protons collide with antiprotons at 2 TeV

20. 20

21. 21 Kaluza-Klein dark matter H-S Cheng, J. Feng, and K. Matchev G. Servant and T. Tait if we live in the “bulk” of compact extra dimensions, then Kaluza-Klein parity (i.e. KK momentum) is conserved. could be a KK neutrino, bino, or photon so the lightest massive KK particle (LKP) is stable

22. 22 how heavy is the LKP? current data requires M LKP ~> 300 GeV LKP as CDM wants M LKP ~ 600 – 1200 GeV might be too heavy for the Tevatron, but the LHC collider experiments will certainly see this

23. 23 furthermore, we could have signals from direct searches in the next generation of WIMP detectors

24. 24 recently, we have uncovered some more radical explanations for hidden dimensions: hidden dimensions e.g. it may be that not all particles (in a certain energy range) move, probe, or see the same number of spatial dimensions a dramatic realization of this is called the braneworld

25. braneworlds Standard Model particles are trapped on a brane and can’t move in the extra dimensions only gravitons and exotics move in the “bulk” of the extra dimensional universe

26. 26 in the most extreme version of braneworld, only gravity tells us about the extra dimensions this hides the extra dimensions quite efficiently, since gravity effects are hard to measure… only the graviton (the force particle of gravity) can move off the brane into extra dimensions various kinds of braneworld scenarios are quite natural in string theory

27. 27 gravitons may be our only probe of extra dimensions but gravity is so weak that we have never even seen a graviton. The gravitational attraction between two electrons is about 10 42 times smaller than the electromagnetic repulsion. F=G N m electron r 2 r m electron

28. 28 gravity gets stronger at extremely high energies M Planck = 10 19 GeV (or very short distances) force strength energy 4d gravity (4+n)d gravity it gets stronger at not-so-high energies (not-so-short distances) if there are extra dimensions…. extra dimensions change gravity

29. 29 ADD braneworld models Arkani-Hamed, Dimopoulos, Dvali assume that only gravity sees n large extra compact dimensions with common size R: in ADD models M * ~ 1 TeV, in order to eliminate the hierarchy problem of the Standard Model. This energy scale is perhaps in reach of the Fermilab Tevatron

30. 30 Solar system Pinhead Gold atom these are large extra dimensions we can test these models in a variety of experiments

31. 31 force laws single photon exchange single graviton exchange both give 1/r potentials

32. 32 force laws if extra dimensions appear at some length scale R, exchange of massive graviton KK modes gives additional Yukawa potentials  e -r/  r look for these deviations in short-range gravity expts

33. 33 Eot-WashGroup : no deviations seen at ~200 microns

34. 34 still possible to see something at ~ 10 microns

35. 35 astrophysics and cosmology constrain ADD (or other) models with too many low mass KK gravitons lower bounds on M *, in TeV

36. 36 quantum gravity at colliders if ADD is correct collider expts should see effects of both real and virtual massive KK gravitons

37. 37 quantum gravity at colliders because we are on a brane, 2 SM particles can collide to produce a single massive graviton the graviton “escapes” the graviton “escapes” into the extra dimensions into the extra dimensions gluon (becomes jet of hadrons) graviton quark antiquark

38. 38

39. 39 tree diagrams for qqbargraviton + gluon implemented in PYTHIA

40. 40 these gravitons are heavy!

41. 41 CDF simulation courtesy M. Spiropulu

42. 42 now let’s look at real data from the Tevatron: Caveat: while the monojet signature is spectacular, it can be mimicked by several Standard Model processes

43. 43 CDF preliminary

44. 44 CDF preliminary

45. 45

46. 46 Angular distributions ATLAS can distinguish spin 2 vs 1 up to 1.72 TeV graviton has spin 2 M=1.5 TeV 100fb -1 B.C. Allanach, K. Odagiri, M.A. Parker, B.R. Weber (JHEP 09 (2000) 019 – ATL-PHYS-2000-029) gravitons at the LHC

47. 47 virtual KK graviton exchanges will interfere with SM diagrams in a variety of processes theory treatment is slightly bogus because sum of KK modes is sensitive to details of the real UV theory

48. 48

49. 49 Randall–Sundrum warped space zero mode graviton likes to be near mother, but Kaluza-Klein graviton modes do not mother brane G weak brane 5th dimension

50. 50 in warped space, it is natural for gravity to be weak if we live anywhere but the “mother brane”, gravity will seem weak gravity is weak because of small probability for graviton to be near the weak brane on the weak brane the mass hierarchy of the Standard Model becomes natural this scenario is testable at high energy colliders

51. 51 compactified space: R <~ 10 -16 cm ADD braneworlds: R <~ 200 microns warped braneworld : R <= infinity! the warped braneworlds hide the extra dimensions even more efficiently than ADD braneworlds: current experimental upper bounds on the size of extra dimensions:

52. 52 collider signals can also be dramatically different H. Davoudiasl, J. Hewett, T. Rizzo

53. 53 science fiction, science fact although extra dimensions is a pretty weird concept, physics has already produced many even weirder phenomena the real leap of imagination is designing experiments to explore the extra dimensions - if they exist.

54. 54 Large Hadron Collider (CERN, 2007) new accelerators for new physics

55. 55 new accelerators for new physics Linear Collider

56. 56 long ago philosopher Immanuel Kant gave a ~500 page proof that space and time are a priori however to make sense of quantum gravity, not to mention the Big Bang singularity, this cannot be true in the real theory of everything, spacetime should be emergent. emergent spacetime

57. 57 emergent spacetime a great theoretical challenge for the future is to figure out where spacetime comes from in the first place spacetime must somehow arise “dynamically”, but what does dynamics mean without spacetime?

58. 58 what is a dimension, anyway? a good starting point is to realize that, operationally, an extra dimension of space just means new degrees of freedom of a certain type (Kaluza-Klein modes). but we already have discovered examples in string theory (e.g. AdS/CFT) where new degrees of freedom can be interpreted either as an extra dimension or as new dynamics without an extra dimension!

59. 59 deconstructing dimensions recently we have even discovered how to do this in simple models that do not carry all the heavy baggage of full-blown string theory these “deconstruction models” are a first step to a more dynamical understanding of spacetime dimensions N. Arkani-Hamed, A. Cohen, H. Georgi H-C Cheng, C. Hill, S. Pokorski, J. Wang particle theorists are learning to think differently…

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