Lisa Randall , Harvard University Entering Ne w Er a

„ MhllLHChMany challenges as LHC approaches „ Critical questions: „ Are we optimizing existing searches? „ Are we doing all the searches possible? „ MdlModels „ LowerLower--Scale:Scale: Supersymmetry, Little Higgs „ HigherHigher--Scale:Scale: Strongly Interacting theories, Extra dimensions „ Focus today on extra dimensions „ Bonu s: Way to lear n abou t qu antum g ra vit y and strongly interacting physics OUTLINE OF TALKS

„ Lecture 1: Introduction to RS1 „ Motivation „ Original Model „ KK signatures of original model „ Lecture 11--22 Bulk RS „ KK Signatures when bulk gauge bosons, fermions „ Lecture 2 „ Black Holes from Extra Dimensions „ Lecture 3 „ Flavor from Warped Extra Dimensions

MtitiMotivations f or N ew Dimens ions

„ String theory: extra dimensions essential „ Lower energies: Extra dimensions can illuminate connections among observable phenomena in new ways „ General Relativity works for any number of dimensions „ Plus: „ Bonus: Even shed liggpyht on purely fourfour-- dimensional physics A New View of Weak Scale Physics

„ Manyypyy new results in physics in last ten years „ Some of the most exciting involve extra dimensions of space „ Intriguing possibilities for our universe: both theoretical and experimental „ Warppged geometry ypy plays a central role in string theory today „ Warped geometry has particularly interesting signatures: resonances! „ Critical to explore theoretical possibilities and experimental consequences What’s New ? Br anes

Branes: Distinguish dimensions along a brane from those perpendicular to it Important Phenomeno logi cal/M od el -Bu ilding Implications 1) Don’t need curled up dimensions to get small extra dimension 1) Can be bounded by branes Before Branes, CCldurled--upup Dimensi on onl y W ay t o Hide Dimension

Idea is that something small is invisible Here the small thing is a dimension of space Entire universe is curled up! Dimensions you observe depend on siiize: Two dimensions for a small bug

rc One dimension for a bigger (ltit(relative to roll llded--upup dimensi on) bug

rc Bou nded b y B ranes

rc Important Phenomeno logi cal/M od el -Bu ilding Implications 1) Don’t need curled up dimensions to get small extra dimension 1) Can be bounded by branes

2) Not all matter travels in bulk; BRANEWORLD 1) Not necessarily KK mode of electron, photon 2) Extra Dimensions can be much bigger than thought Particles can be stuck on a brane Like W at er d ropl et s on “ sh ower brane” „ LowerLower--dimensionaldimensional surface in higherhigher-- dimensional space „ Shower curtains trap things (water droplets) on lower-lower- dimensional surfaces. „ Similarly, particles can be confined to a three-dimensional brane BaneoldBraneworld HigherHigher--dimensionaldimensional world in which particles and matter are st uck on a b rane

Drawn as 2D Really 3D And really ifiitinfinite

The boundary brane might house matter, particles; or could be brane inside bulk Important Phenomeno logi cal/M od el -Bu ilding Implications 1) Don’t need curled up dimensions to get small extra dimension 1) Can be bounded by branes

2) Not all matter travels in bulk; BRANEWORLD 1) Not necessarily KK mode of electron, photon 2) Extra Dimensions can be much bigger than thought

3) Warping permits even infinite dimension 1) Gravityyg gets localized With branes, we’ve found warped geometry solutions that provide:

„ New way to hide dimensions

„ NtflithiNew concept of our place in the universe

„ New way to explain weakness of gravity Connection to Ph ysics Hierarch y P robl em:

„ Why is gravity so weak compared to the other elementary forces?

Might not seem weak but magnet can take on the entire Earth- Hierarch y P robl em Need “fine-tuning” to get very different masses Key issue in particle physics today One that will be resolved at LHC “Fine-tuning” is unlikely:

Barnett Newman: Broken Obelisk With Raman RS1 “Multiverse:” Sundrum Warped Spacetime Geometry

•Two branes •Gravity will be concentrated on Gravitybrane •But we live on a second brane: •The Weakbrane/TeV Brane Natural for gravity to be weak!

„ Small probability for graviton to be near the Weakbrane

„ If we live anywhere bhGibbut the Gravitybrane, gravity will seem weak

„ Natural consequence of warped geometry RliARescaling Across Fifth FifthDii Dimension

m_->e-kr m

Important for phenomenology: weak scale physics Higgs mass r escaled

„ Kinetic term has 2 powers of warp factor „ Mass term has 4 „ Result is mass rescaled „ In fact warp factor is like conformal factor

„ So…if modes localized near TeV brane „ Expect TeV mass „ TttbtfKKd!Turns out to be true for KK modes!

How to test?

„ Search for new particles! Everything near weak brane should have TeV mass

„ KaluzaKaluza--KleinKlein (KK) particles

„ Carry momentum in extra dimensions

„ Looks like mass in 4 dimensions

„ Connection to mass and weakness of ggyravity relative to other known forces tells us

„ LHC will have the right energy to search for consequences of this theory Exppgerimental Signal: TeVTeV--scalescale Graviton Resonances!

Protons collide LHC Collision „ Produce a Kaluza - Klein particle

„ Which Decays proton eltlectron „ Definite mass spectrum and “spin”“spin”--22 positron

proton How to find KK masses and interactions

„ Solve equations of motion

„ Bessel function solutions

„ Impose two boundary conditions at branes

„ OiOne gives correct tli linear combi bitination

„ Second gives quantization condition Wavef u nction Equation Change va riables

Volcano potential: ‘quant um mechanics’ potential Find sol ution Impose Bo unda ry Conditions KK modes

„ Find modes at every mass scale

„ However essentially linearly quantized in --krkr multiples of ke c within mass range of order m (cutoff)

„ That is (m/k) modes in our vicinity

„ TthlktlittitTo us theory looks strongly interacting at TeV

„ (not true for full 5d theory) TeV scale KK 1012 TeV Mode 1000 TeV modes mode Observable KK modes

„ In RS1, KK spectrum very distinctive

„ TeV,,, 2 TeV, 3 TEV ( (g)prough) spectrum

„ TeeV scal e m odes l ocaliz ed on w eak br an e

„ Have “warped” gravitational interaction

„ So 1/TeV scale graviton interaction with

Standard Model particles (not 1/MPl) „ Much stronger than gravitational! Exppgerimental Signal: Can search for extra dimensions!

Protons collide LHC Collision „ Produce a Kaluza - Klein particle

„ Which Decays proton eltlectron „ Definite mass spectrum and “spin”“spin”--22 positron

proton „ If you produce a KK mode of the gravition „ Not just missing energy! „ Mode decays inside detector —just like most other heavy particles we hope to discover 9 Means we can reconstruct mass, spin (we hope!) 9 Would be first genuine signature of quantum gravity 9 Graviton itself too weakly interacting to detect directly 9 Not true for its KK modes! Search for Resonances

H. Davoudiasl, J. Hewett, T. Rizzo Reach for Gr av iton KK Modes

Davoudiasl, Hewett, Rizzo graviton has spin 2

M=1.5 TeV 100fb-1

AldiibiAngular distributions „ RS1 gives clean TeVTeV--KKKK--gravitongraviton signal „ One of first things LHC could find „ Spinpin--2d2 and gap in spectrum d dfefinite ind ication of warped extraextra--dimensionaldimensional geometry „ Could also exist stronggyly interacting TeVTeV--scalescale ppyhysics to complement this measurement „ Even low scale quantum gravity or light string states could appear (we ’ ll return to this) „ But not the only implementation of RS1 mechanism „ What d oes thi s i mpl y ab out search st rat egi es?

Variations on RS1: Infinite extra dimension

IfiitdiInfinite dimeni son

weakbrane Missing Ene rg y Signal

„ Looks like 6 large dimensions

„ In this case KK mode decays to lighter KK modes

„ KK energy goes to missing energy „ Variations of RS1: matter in bulk or on brane??

„ Two key features that make bulk matter possible

¾ Size of fifth dimension extremely small (only about 30 times fundamental scalescale—— exponential hierarchy) Means coupling won’t be too diluted/weak

¾ You only need Higgs on the Weakbrane to address the hierarchy

™ Problem only for the Higgs scalar: gauge boson and fermion masses are protected Merits of bulk fermions and gggauge fields

„ 5D cutcut--offoff is Planck scale

9 Allows for unification!

„ Also interesting modelmodel--building:building:

9 Fermion masses fffrom wavefunction over lap with Higgs field (on Weakbrane)

„ W’llWe’ll see th thtblkat bulk scenari os h ave distinctive signatures Modes at All Ene rgies

TeV scale KK 1012 TeV Mode 1000 TeV modes mode Bu lk Unification „ Net contribution from all modes

„ Gives logarithmic running

„ From TeV scale to Planck scale

„ LESSON 2: very natural to have unification

Gravity Coupling energy strength energy Fermion masses from wavefunctions

„ Might expect nontrivial profiles

„ Masses depend on overlap with Higgs

„ Expect light fermions localized near Planck/Gravity brane

„ Top near Weakbrane since it’s heavy

u ,d L L tR Flavo r hie ra rchies φ „ z~ekr

„ dzf= (M /k+1 /2) f ν „ f~z φ „ f~e kr (M/k+1/2) „ M/k=ν<-1/2 : light quarks

„ ν>>--1/2:1/2: top quark BlkRSBulk RS

„ Variation of RS1: fermions and gauge bosons in bulk

„ Hierarchy just like before

„ But flavor , unification possibilities However: Important Differences in Phenomenol ogy f rom B ranerane-- Localized Matter „ Richer Spectrum „ KK modes of „ Weak bosons „ Gluons „ Fermions „ As well as gravitons

„ But…lower Production Cross Section for Graviton „ Plus decays primarily into tops „ Changes search strategies dramatically Gluon , Gl uon KK WFs

Planck brane

Kk Gluon graviton wavefunction

Gluon KK wavefunciton TeV brane Richer Spectrum… But Lower Production Cross Section for the Graviton „ LiLight ht quark s are l ocali zed away f rom Higgs

„ Hence away from TeV brane

„ No DrellDrell--YanYan production from quarks

„ Gluons are spread throughout the bulk

„ Hence coupling to graviton is volume suppressed Gr av iton Interactions

Volume O(1), 1/ k¼r ;suppressedor 0 c Gr av iton inte r actions Featur es of inter actions

„ The suppression by M4L is a factor of 1/N from the dual gggauge theory ypp perspective μ „ 1/ TeV is local cutoff

„ 1/krc because gluon has flat wave function: volume factor

„ FibhiFermion behavior w/Liam Fitzpatrick,Jared Kaplan, Liantao KK G r av iton P r oduction Wang Final State? Dominant Decay to rightright--handedhanded tops

More narrow

Determininggpj top jets: delta R: Angle between decay products Anggpular dependence: sp in determination Graviton: some reach Other Bulk Modes? Gluon , Gl uon KK WFs

Planck brane

Kk Gluon graviton wavefunction

Gluon KK wavefunciton TeV brane Gluon KK Mode!

„ Gluon KK mode coupling to light quarks is much bigger than graviton „ Gluon KK mode wave function peaked at TeV brane „ BtBut re ltillatively fl fltiat in b blkulk; „ Only square root volume „ Also expect gl luon KK mod e light li hter b y factor 1.5 „ Finall y no 1/M „ Much larger reach for gluon KK mode Understand from dual point of view in terms of gluon KK mixing-vector meson dominance

Note only gluon production from quarks. At tree level, gluon coupling vanishes. Gluon wave function KK Gluon fermion interaction

(relative to gs) w/Ben Lillie, Liantao Wang DDitominates over tjtbktop jet backgroun d However,,g signal doesn’t dominate over jet background Top dete rmination : dR?

Clearl y…

„ Efficient top jet identification required, esppyecially for heavier KK g luons

„ Could be:

„ Top jet mass measurement

„ Detailed substructure of jets: eg hard lepton

„ Beyond our study

„ But can determine accuracy with which determination is required Conclude require at most 10% fake rate Spin Dete rmination

Forward region significance enhanced with pt cut For ligg,ht masses, can determine

model structure: tR

Angle between lepton and top momentum axis Su mmary

„ Weak scale physics should be testable at LHC

„ Includingg, RS1, whatever the imp lementation

„ Best signature: spinspin--22 resonance and mass gap

„ In bulk, g luo n KK mode will be impo rta nt

„ Decays into tops critical

„ Challenge is to maximize energy reach

„ But hope for pinning this down To be done

„ Think about jet characteristics

„ Detailed substructure

„ Push b tagging to limit

„ Explore hard leptons Conclude

„ If RS1 solves the hierarchy problem, we should be able to tell

„ Clean KK graviton signal if SM on brane

„ Far-reaching KK gluon signal if SM in bulk

„ Supplemented by graviton KK signal if suffic ientl y l ow scal es

„ But challenges: top quark ID foremost!