Extra Dimensions Primer (see S. Hossenfelder) LED in many dimensions JLH, Lillie, Rizzo hep-ph/ SUSY05 DurhamJ. Hewett

Models with Large Extra Dimensions Arkani-Hamed, Dimopoulos, Dvali 1998 Gravity in the bulk D = 4 + n SM confined to brane Fundamental scale of gravity in bulk = M * Gauss’ Law: M * ~ TeV ‘solves’ hierarchy ! R c ~ 0.1 mm to 1 fm for n = Graviton KK states finely spaced m KK 2 = n 2 /R c 2 m 1 ~ eV to MeV for n = Collider Signatures Graviton KK Emission Graviton KK Exchange Black Hole Production

Current Experimental Constraints M D ~ 1 TeV from Graviton exchange and emission at LEP II and Tevatron: Updates this afternoon! Tabletop: R c < 130 microns for  = 2, or M D > 1.7 TeV Hoyle etal hep-ph/

Astrophysics Constraints: Reexamined Supernova Cooling NN  NN + G n can cool supernova too rapidly Cosmic Disfuse Gamma-rays G n  (Expect Big improvements from GLAST!) Neutron Star Heat Excess NN  NN + G n becomes trapped in neutron star halo Hannestad and Raffelt (See also Casse etal)

TeV -1 Extra Dimensions The Standard Model goes into the bulk! Many model building choices: –Gauge fields in the bulk –Higgs in bulk or brane –Fermions: located at orbifold fixed points localized at specific points: Split Fermions propagate freely through bulk: Universal ED Phenomenology greatly depends on fermion locations!

Experimental Constraints on TeV -1 ED Fermions at orbifold fixed points –Precision EW with KK gauge exchange: M c > 4 TeV –LEP II indirect KK gauge exchange: M c > 3 TeV Split Fermions –Precision EW with KK gauge exchange: M c > 2-3 TeV –Tree-level FCNC with KK gauge exchange: Generally M c > 100’s TeV, but can arrange for M c > few TeV Universal ED (KK parity is conserved) –Precision EW from loop contributions: M c > 300 GeV –Pair production of KK states: M c > few 100 GeV (Updates this afternoon?) Huge number of contributing authors!

Randall-Sundrum model of Localized Gravity Graviton KK states: m n = x n   k/M Pl ; J 1 (x n ) =0 TeV-scale masses with TeV -1 couplings to SM Bulk is slice of AdS 5 ds 2 = e -2ky   dx  dx -dy 2   = e -kr  M Pl ( = TeV-scale

Experimental Constraints on RS Gravitons Graviton resonances in Drell-Yan and diphoton –Updates this afternoon! Indirect Graviton searches LEP II Tevatron

LED: Is the hierarchy problem really solved? M * R c > 10 8 for n = 2-6 Disparate values for gravity and EWK scales traded for disparate values of M * and R c However, 1 < M * R c < 10 for n = Large n offers true solution to hierarchy!

Collider Signatures Change Graviton KK states are now ‘invisible’ m 1 ~ TeV Couplings are still M Pl -1 Collider searches are highly degraded! For n = 2, M * up to 10 TeV observable at ILC, LHC Drops to < 1 TeV for n = 20 Only viable collider signature is Black Hole production!

Black Hole LHC: Black Holes produced when  s > M * Classical Approximation: [space curvature << E] E/2 b b < R s (E)  BH forms M BH ~  s ^ Geometric Considerations:  Naïve =  R s 2 (E), details show this holds up to a factor of a few Dimopoulos, Landsberg Giddings, Thomas

Production rate is enormous! 1 per sec at LHC!  Naïve ~ n for large n M * = 1.5 TeV

Potential Corrections to Classical Approx: 1.Distortions from finite R c as R s  R c 2. Quantum Gravity Effects Higher curvature term corrections Critical point for instabilities for n=5: (R s /R c ) 2 ~ LHC Gauss-Bonnet term R S 2 /(2  R c ) 2 n = n =  n 2 ≤ 1 in string models

Potential Corrections to Classical Approx: 1.Distortions from finite R c as R s  R c 2. Quantum Gravity Effects Higher curvature term corrections Critical point for instabilities for n=5: (R s /R c ) 2 ~ 0.1 LHC) R S 2 /(2  R c ) 2 n = n =  n 2 ≤ 1 in string models Note: This defines M *

Decay Properties of Black Holes (after Balding): Decay proceeds by thermal emission of Hawking radiation At fixed M BH, higher dimensional BH’s are hotter:  N  ~ 1/  T   higher dimensional BH’s emit fewer quanta, with each quanta having higher energy Harris etal hep-ph/ Multiplicity for n = 2 to n = 6 n determined to  n = 68% CL for n=2-6 from T H and  This procedure doesn’t work for large n

p T distributions of Black Hole decays Provide good discriminating power for value of n Generated using modified CHARYBDIS linked to PYTHIA with M * = 1 TeV

Determination of Number of Large Extra Dims Perform  2 fit assuming M * = 1 TeV and n = 21 Generated 300k events (~ 10 fb -1 ) Used p T missing distb’n only Discrimination improves when jet p T included as well n < 6(7) excluded at 5  for n > 13 Excellent resolution power for large values of n!

Motivations for determining value of n: It’s a property of Extra Dims that we will want to know; provides a handle on the physics of Quantum Gravity Distinguishes BH’s from large flat extra dims from those in Randall-Sundrum warped models (n = 1) Provides null test of Critical String Theory!!! If string theory is correct, large extra dims will be embedded in it and M s ~ TeV String resonances may be produced at LHC (if weak heterotic strings), but do not provide determination of n CST requires n = 6(7) for anomaly cancellation Determination of n > 6(7) from Black Hole production would exclude CST as a string theory candidate! Black Holes provide collider information on string theory

In Summary: There are lots of possibilities for New Physics at the TeV scale We haven’t (yet) thought of most of them The LHC will make many great discoveries We have exciting times ahead of us!