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mysteries of extra dimensions Joseph Lykken Fermi National Accelerator Laboratory 1 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 2 the universe: traditional view 3 the universe: a bigger view extra dimensions of space everything we know about is on this slice the rest is terra incognita 4 questions for this talk 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? 5 why do physicists think that there are extra dimensions of space? Reason #1: string theory particle physicists developed string theory to understand quantum gravity - to explain extreme physics such as goes on inside black holes supermassive black hole in the center of galaxy M87 6 string theory in string theory, all the elementary particles are merely different vibrations of a single substance called strings. 7 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! 8 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? 9 in string theory the answer lies in the shape of the extra dimensions slice of a 6 dimensional CalabiYau space 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. 10 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 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 drove cosmic inflation in the early universe 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 this was 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 extra dimensions may be the extra ingredient that explains the history of the universe 14 hidden dimensions if extra spatial dimensions exist, they must be (for some reason) difficult to probe physicists have uncovered several possible explanations: e.g. the extra spatial dimensions are compact and small Nordstrom, Kaluza, and Klein, circa 1920 15 compact extra dimensions what do we look for experimentally?… 16 Kaluza-Klein modes if spatial dimension is compact then momentum in that dimension is quantized: n p R from our point of view we see new massive particles! m 2 m02 n2 4 R R2 3 R KK momentum tower of states 2 R p 1 R 0 17 how do we look for Kaluza-Klein particles? 18 21st century particle physics Fermilab’s Tevatron is the highest energy accelerator in the world today. protons collide with antiprotons at 2 TeV 19 20 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. so the lightest massive KK particle (LKP) is stable could be a KK neutrino, bino, or photon 21 how heavy is the LKP? current data requires MLKP ~> 300 GeV LKP as CDM wants MLKP ~ 600 – 1200 GeV might be too heavy for the Tevatron, but the LHC collider experiments will certainly see this 22 furthermore, we could have signals from direct searches in the next generation of WIMP detectors 23 hidden dimensions recently, we have uncovered some more radical explanations for 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 24 braneworlds only gravitons and exotics move in the “bulk” of the extra dimensional universe Standard Model particles are trapped on a brane and can’t move in the extra dimensions various kinds of braneworld scenarios are quite natural in string theory in the most extreme version of braneworld, only gravity tells us about the extra dimensions only the graviton (the force particle of gravity) can move off the brane into extra dimensions this hides the extra dimensions quite efficiently, since gravity effects are hard to measure… 26 gravitons may be our only probe of extra dimensions but gravity is so weak that we have never even seen a graviton. melectronmelectron F=GN r2 melectron r melectron The gravitational attraction between two electrons is about 1042 times smaller than the electromagnetic repulsion. 27 extra dimensions change gravity gravity gets stronger at extremely high energies MPlanck = 1019 GeV (or very short distances) it gets stronger at not-so-high energies (not-so-short distances) if there are extra dimensions…. 28 ADD braneworld models Arkani-Hamed, Dimopoulos, Dvali assume that only gravity sees n large extra compact dimensions with common size R: M 2 Planck n ~R M n 2 * 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 29 these are large extra dimensions n 1 R ~ 109 Km n2 R ~ 1mm Pinhead n3 R ~ 1nm Gold atom n 6,7 Solar system R ~ 10 fm we can test these models in a variety of experiments 30 force laws single photon exchange single graviton exchange both give 1/r potentials 31 force laws if extra dimensions appear at some length scale R, exchange of massive graviton KK modes gives additional Yukawa potentials a e-r/l/r look for these deviations in short-range gravity expts 32 : Eot-Wash Group no deviations seen at ~200 microns 33 still possible to see something at ~ 10 microns 34 lower bounds on M* , in TeV astrophysics and cosmology constrain ADD (or other) models with too many low mass KK gravitons 35 quantum gravity at colliders if ADD is correct collider expts should see effects of both real and virtual massive KK gravitons 36 quantum gravity at colliders because we are on a brane, 2 SM particles can collide to produce a single massive graviton quark gluon (becomes jet of hadrons) antiquark graviton the graviton “escapes” into the extra dimensions 37 38 tree diagrams for qqbar graviton + gluon implemented in PYTHIA 39 these gravitons are heavy! 40 CDF simulation courtesy M. Spiropulu 41 Caveat: while the monojet signature is spectacular, it can be mimicked by several Standard Model processes now let’s look at real data from the Tevatron: 42 CDF preliminary 43 CDF preliminary 44 45 gravitons at the LHC graviton has spin 2 M=1.5 TeV 100fb-1 Angular distributions ATLAS can distinguish spin 2 vs 1 up to 1.72 TeV B.C. Allanach, K. Odagiri, M.A. Parker, B.R. Weber (JHEP 09 (2000) 019 – ATL-PHYS-2000-029) 46 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 47 48 Randall–Sundrum warped space G mother brane 5th dimension zero mode graviton likes to be near mother, but Kaluza-Klein graviton modes do not 49 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 50 the warped braneworlds hide the extra dimensions even more efficiently than ADD braneworlds: current experimental upper bounds on the size of extra dimensions: compactified space: ADD braneworlds: warped braneworld : R <~ 10-16 cm R <~ 200 microns R <= infinity! 51 collider signals can also be dramatically different H. Davoudiasl, J. Hewett, T. Rizzo 52 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. 53 new accelerators for new physics Large Hadron Collider (CERN, 2007) 54 new accelerators for new physics Linear Collider 55 emergent spacetime 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. 56 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? 57 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! 58 deconstructing dimensions N. Arkani-Hamed, A. Cohen, H. Georgi H-C Cheng, C. Hill, S. Pokorski, J. Wang 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 particle theorists are learning to think differently… 59 60