Lisa Randall, Harvard University

A New View of Weak Scale PhysicsMany new results in theoretical physics Some of the most exciting involve extra dimensions of spaceIntriguing possibilities for our universe: both theoretical and experimentalWarped geometry has particularly interesting signatures: resonances!Extra dimensions of space could be the next big discovery at CERN

Sampling of what we now know is possiblein physics!Braneworlds and MultiversesExtra dimensions can be infinitely large, yet be invisibleNew place in the universe: three-dimensional sinkholeExtra dimensions can illuminate connections, resolving puzzles of a 3+1 dimensional worldWith testable experimental consequences

Why should such different results connect?High-energy physics covers an enormous range of energiesAt the highest energies, we need a theory of quantum gravitya theory that includes quantum mechanics and general relativityString theory, in which the fundamental ingredients are oscillating, vibrating strings, is the leading candidate

Lower Energies?At lower energy scales, there are physical phenomena that we can study experimentallyUnderstand basic elements of matter and their interactionsNew ideas might provide deeper connections among known physical quantities: masses, forcesThese are theories we can experimentally test

The best route? Model Building: adventure travel through world of ideas

Extra Dimensions One Route?String theory: extra dimensions essential Lower energies: Extra dimensions can illuminate connections among observable phenomena in new ways They are after all a possibility from perspective of general relativityPlus:Bonus: Even shed light on purely four-dimensional physics

Extra Dimensions in PhysicsTheodor Kaluza proposed extra dimensions in 1919Einstein (referee) delayed publication for two yearsInteresting idea, but what makes the other dimension different?Old answer: Extra dimensions can be rolled up to a tiny sizeBut Also New Answers

Hose Across Football Field1 DimensionalCan see 2D or 3D with small probeVery intuitive; if sufficiently tiny, it doesnt look like its thereOskar Klein proposed idea that dimension is rolled up in 1926If a dimension is wound sufficiently tightly you wont see it

Curled-up DimensionEntire universe is curled up!

New (1999) Way to Hide DimensionsBased on an important ingredient in string theory whose importance was only recently recognizedBRANESMembrane-like objects in higher dimensional spacePlay an essential role in string theory

Whats New? BranesBranes:Distinguish dimensions along a brane from those perpendicular to it

Branes can trap particles and forcesStuck on a brane like a bead on a wireParticles stuck on a brane like beads on a wire

D-Branes: Where Open Strings EndParticles and forces stuck on branesnot gravity!

Why not gravity?Gravity ---closed string: no ends!

Energy: all energy interacts via gravity

Geometry: gravity connected to spacetime

BraneworldDrawn as 2DReally 3DAnd reallyinfiniteHigher-dimensional world in which particles and matter are stuck on a brane

With branes, weve found warped geometrySolutions that provide:New way to hide dimensionsNew way to explain weakness of gravityNew concept of our place in the universe

RS2 Braneworld New way to hide a dimension (LR with Raman Sundrum) Extra dimension can be infinite in size! Spacetime is warped and gravity stays near the brane.

Localized Gravity:Warped Geometry Gravity is concentrated near the braneTiny probability for gravity to leak away from brane We solved equations for gravity and according to Einsteins General RelativityAll of spacetime is warped

Force spreads very asymmetricallyLines of gravitational force almost parallel to braneGravity doesnt leak into extra dimension as you would expect without warpingLocalized gravity: new way to hide dimensions

Gravitational Field Near Brane

Extra dimension can be infinite in sizeWithout us knowing about itBecause warped gravity spreads out in only three spatial dimensions---Not four (really, tiny amount in fourth)

Alternative to rolled-up dimension!

Even More Dramatic: Locality of Four DimensionsWhy should you need to know about space far from the brane?With Andreas Karch, found four-dimensional gravity near the braneBut higher-d everywhere elseFour-dimensional sinkhole

Exciting but frustratingCould exist something as dramatic as an infinite extra dimension, pockets of lower-dimensional space, but we wouldnt know it!Can a warped extra dimension be tested?Yes, if connected to Particle Physics

Hierarchy Problem: One of the biggest puzzles in particle physicsWhy is gravity so weak compared to the other elementary forces?

Might not seem weak but magnet can take on the entire Earth-

Hierarchy ProblemNeed fine-tuning to get very differentmassesKey issue in particle physics todayOne that will be resolved at LHC

Fine-tuning is unlikely:No artist so we need an explanation Barnett Newman: Broken Obelisk

RS1 Multiverse:Warped Spacetime Geometry Like BeforeNow two branesGravity still concentrated on GravitybraneBut we live on a second brane:The Weakbrane

If we live anywhere but the Gravitybrane, gravity will seem weakSmall probability for graviton to be near the WeakbraneNatural consequence of warped geometryNatural for gravity to be weak!

Rescaling Across Fifth Dimension

Everything rescaled in warped geometry!

Can understand weakness of gravity as things being bigger and lighter on the Weakbrane

What rescaling means:Anything on or near the Weakbrane hasOrder TeV-scale massAnything localized in the bulk hasCorrespondingly exponentially bigger massOn Gravitybrane-back to Planck-scale masses

Particles in bulkPlanck 106 TeV 1000 TeV TeV

Experimental Tests?

Connection to mass and weakness of gravity relative to other known forces tells us LHC will have the right energy to search for consequences of this theoryAnything on the Weakbrane should have roughly TeV energy/massMany modes on the TeV/Weakbrane

KK Particles: Weak Scale Fingerprints of Extra DimensionsWith extra dimensions, there are new Kaluza-Klein (KK) particlesTravel and carry momentum in extra dimensionsLook to us like particles with mass characteristic of the extra-dimensional geometry

KK modes of gravitonIn RS1, KK spectrum very distinctiveTeV, 2 TeV, 3 TEV (rough) spectrumWith much stronger than gravitational interaction strength!Interaction strength is warped too!Not 1/MPInstead, 1/TeV

ImplicationsIf you produce a KK mode of the gravitionNot just missing energy!Mode decays inside detectorjust like most other heavy particles we hope to discoverMeans we can reconstruct mass, spin (we hope!)Would be first genuine signature of quantum gravity Graviton itself too weakly interacting to detect directlyNot true for its KK modes!

Experimental Signal: Can search for extra dimensions!

Kaluza-Klein particlesDefinite mass spectrum and spin-2Truly different than other strongly interacting theoriesLight spin-2 but gapNo other strongly interacting states as light

collider signals would be dramatically differentH. Davoudiasl, J. Hewett, T. Rizzo

If RS1 solves the hierarchy problem, we should be able to tellAnd if we are very lucky, five-dimensional black holes and string states might also appear

LESSON 1: RS1 gives clean TeV-KK-gravitonSpin-2 and Gap in spectrum definite indication of warped extra-dimensional geometryLots of strongly interacting TeV-scale physics to complement this measurement

Other warped scenarios addressing the hierarchy?RS1 isnt the only scenario: variations interestingDepends on whether particles on brane or in bulkTwo key features that make bulk matter possibleSize of fifth dimension extremely small (only about 30 times fundamental scaleexponential hierarchy)Means you can have gauge bosons in the bulkCoupling wont be too weakYou only need Higgs on the Weakbrane to address the hierarchyProblem only for the Higgs scalar: gauge boson and fermion masses are protected

Suggests new scenariosFermions and/or gauge bosons can be in the bulkBecause 5D cut-off is Planck scaleAllows for unification!Allows for interesting model-building:Fermion masses from wavefunction overlap with Higgs field (on Weakbrane)Bulk scenarios have distinctive signatures

Particles in bulkPlanck 106 TeV 1000 TeV TeV

Bulk Unification

Net contribution from all modesGives logarithmic running From TeV scale to Planck scaleLESSON 2: very natural to have unificationenergyCouplingstrengthGravity energy

Phenomenology?Bulk gauge bosonsMeans KK modes of weak bosons,gluons as well as gravitonsResonances with strong force interactions for example

Can find gluon KK modes and distinguish number of dimensionsLR with Ben Lillie, Liantao WanghLESSON 2: Resonances have moreInfo than weve explored yet

Precise signatures depend on fermion wavefunction profilesMight expect nontrivial profilesMasses depend on overlap with HiggsExpect light fermions localized near Planck/Gravity braneTop, bottom near Weakbrane

Fermion Profiles and Masses

Dual Interpretation of Warped ScenariosRS phenomenology has dual 4d strongly interacting conformal field theory interpretationRoughly, between Planck scale and TeV scale, CFT At TeV scale, CFT spontaneously brokenGives rise to composite statesWhich states are composite depends on details of wavefunctionThose localized near TeV/Weak brane are more compositeThose localized near Planck/Gravity brane are less composite

Signatures of Partial CompositenessHiggs (longitudinal modes) couplings to electroweak gauge bosons are enhanced

Long W, tR->bL KK resonancesEnhanced KK production through tR loops (Agashe, Delgado, May, Sundrum)Also graviton KK resonance has interactions very similar to that of Higgs! (LR and RS)LESSON 3: RICH PHENOMENOLOGY-NOT YET FULLY EXPLORED

Signatures of Extra Dimensions Still?Still have distinctive spin-2 resonanceWhat other distinguishing features in interactions?Is it extra dimensions or just some strong interactions? gg, gluon gluon interactions should be the same (LR with RS)After all, its a gravitational interactionWorth investigating

One more variant: KR ModelCan have RS without the 2nd brane bounding spacetimeThen get a gapless continuum of KK modesRather than resonance signatures, Reverts to missing energy

Cross Section and Missing EnergyKR: equivalent to n=6SpiropoluMissing energy searches might find KR geometry

Only distinguished by black holes and strings!LESSON 4: Even missing energy searches can find warped scenario

SummaryBest signature: spin-2 resonance and mass gapGood signatures: signals of partial compositenessGreat signature if measurable: relative rate of gg and gluon gluon: indicates warped extra dimensionPlus possible missing energy signature if infinite extra dimensionLots of phenomenologyMuch still to be worked outBut we really want to be able to pin this down

Entering a new era in physicsEvery time weve explored smaller or larger length scales, weve found new phenomena, new connectionsMany exciting new ideas for what we might discoverMore connections are therewe just have to find themSecrets of the universe are about to unravel

Hidden riches in the universe