Extra Dimensions

• Primer (see S. Hossenfelder)

• LED in many dimensions JLH, Lillie, Rizzo

hep-ph/0503178

SUSY05 Durham J. Hewett

Models with Large Extra DimensionsArkani-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 !

Rc ~ 0.1 mm to 1 fm for n = 2 - 6Graviton KK states finely spacedmKK

2 = n2/Rc2

m1 ~ eV to MeV for n = 2 - 6

Collider Signatures

•Graviton KK Emission•Graviton KK Exchange•Black Hole Production

Current Experimental Constraints

• MD ~ 1 TeV from Graviton exchange and emission at LEP II and Tevatron: Updates this afternoon!

• Tabletop:

Rc < 130 microns for = 2, orMD > 1.7 TeV

Hoyle etal hep-ph/0405262

Astrophysics Constraints: Reexamined

• Supernova CoolingNN NN + Gn can cool supernova too rapidly

• Cosmic Disfuse Gamma-raysGn (Expect Big improvements from GLAST!)

• Neutron Star Heat ExcessNN NN + Gn 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 fermionlocations!

Experimental Constraints on TeV-1 ED

• Fermions at orbifold fixed points– Precision EW with KK gauge exchange: Mc > 4 TeV

– LEP II indirect KK gauge exchange: Mc > 3 TeV

• Split Fermions– Precision EW with KK gauge exchange: Mc > 2-3 TeV

– Tree-level FCNC with KK gauge exchange: Generally Mc > 100’s TeV, but can arrange for Mc > few

TeV

• Universal ED (KK parity is conserved)– Precision EW from loop contributions: Mc > 300 GeV

– Pair production of KK states: Mc > few 100 GeV

(Updates this afternoon?)Huge number of contributing authors!

Randall-Sundrum model of Localized Gravity

Graviton KK states:

mn = xn k/MPl; J1(xn) =0

TeV-scale masses withTeV-1 couplings to SM

Bulk is slice of AdS5

ds2 = e-2ky dxdx -dy2

= e-kr MPl (

= 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*Rc > 108 for n = 2-6Disparate values for gravity and EWK scales traded for disparate values of M* and Rc

However,1 < M*Rc < 10 forn = 17 - 40

Large n offers true solution to hierarchy!

Collider Signatures Change

Graviton KK states are now ‘invisible’•m1 ~ TeV•Couplings are still MPl

-1

Collider searches are highly degraded!

For n = 2, M* up to 10 TeVobservable at ILC, LHC

Drops to < 1 TeV for n = 20

Only viable collider signature is Black Hole production!

Black Hole Production @ LHC:

Black Holes produced when s > M*

Classical Approximation: [space curvature << E]

E/2

E/2b

b < Rs(E) BH forms

MBH ~ s^

Geometric Considerations:

Naïve = Rs2(E), details show this holds up to a factor

of a few

Dimopoulos, LandsbergGiddings, 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 Rc as Rs Rc

2. Quantum Gravity EffectsHigher curvature term corrections

Critical point forinstabilities for n=5:(Rs/Rc)2 ~ 0.1 @ LHC

Gauss-Bonnet term

RS2/(2Rc)2

n = 15 - 40

n = 2 - 20

n2 ≤ 1 in string models

Potential Corrections to Classical Approx:

1. Distortions from finite Rc as Rs Rc

2. Quantum Gravity EffectsHigher curvature term corrections

Critical point forinstabilities for n=5:(Rs/Rc)2 ~ 0.1 (@ LHC)

RS2/(2Rc)2

n = 15 - 40

n = 2 - 20

n2 ≤ 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 MBH, 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/0411022

Multiplicity for n = 2 to n = 6

n determined to n = 0.75 @ 68% CL for n=2-6 from TH and This procedure doesn’t work for large n

pT 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 pT missing distb’n only•Discrimination improves when jet pT 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 Ms ~ 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 cancellationDetermination 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!