The Search for Supersymmetry

• Introduction the Standard Model of Particle Physics • Introduction to Collider Physics • Successes of the Standard Model • What the Standard Model Does Not Do • Physics Beyond the Standard Model • Introduction to Supersymmetry • Searching for Supersymmetry • Dark Matter Searches • Future Prospects • Other Scenarios • Summary

Peter Krieger, Carleton University, August 2000 Force Unifications

Standard Model does NOT account magnetism for gravitational interactions Maxwell electromagnetism

electricity electroweak S T A Planck Scale (or Planck Mass) weak interactions N D A is defined as the energy scale at R GUT D which gravitational interactions M O become of the same strength as D E SM interactions strong interactions L TOE celestial movement gravitation Newton terrestrial movement - - -

MEW MGUT Mplanck The Standard Model

Describes the FUNDAMENTAL PARTICLES and their INTERACTIONS

All known FORCES are mediated by PARTICLE EXCHANGE

a a Effective strength of an interaction depends on X • the coupling strength at the vertex αα • the mass of the exchanged particle MX a a

Force Effective Strength Process Strong 100 Nuclear binding

Electromagnetic 10-2 Electron-nucleus binding

Weak 10-5 Radioactive β decay The Standard Model SPIN-½ MATTER PARTICLES interact via the exchange of SPIN-1 BOSONS MATTER PARTICLES – three generations of quarks and leptons |Q| m < m < m ⎛ e ⎞ ⎛ µ ⎞ ⎛ τ ⎞ 1 e µ τ Mass increases with generation: ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ m = 0 ⎜ ⎟ ⎜ν ⎟ ⎜ ⎟ ν ⎝ν e ⎠ ⎝ µ ⎠ ⎝ν τ ⎠ 0 Mu,d ~ 0.3 GeV ⎛u⎞ ⎛c⎞ ⎛ t ⎞ 2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 3 Each quark comes in 1 three ‘colour’ changes Mt ~ 170 GeV ⎝d⎠ ⎝s⎠ ⎝b⎠ 3

GAUGE BOSONS – mediate the interaction of the fundamental fermions

γ 1 Gauge particle of electromagnetism (carries no electric charge) W ± ,Z 0 3 Gauge particles of the weak interaction (each carries weak charge) g 8 Gauge particles of the strong interaction (each gluon carries a colour and an anti-colour charge charge)

All Standard Model fermions and gauge bosons have been experimentally observed

There is one more particle in the SM – the Higgs Boson. This is vital to the SM but remains experimentally undetected Spontaneous Symmetry Breaking

Initial Attempts to unify the weak and electromagnetic interactions failed because while M( γ ) = 0 , the relative strength of the weak interaction requires

M(weak gauge boson) ~ 100 GeV

The SM is formulated in terms of MASSLESS particles Introduction of explicit mass terms destroys a vital property of the theory

In the SM, masses for the weak interaction gauge bosons are generated via SPONTANEOUS SYMMETRY BREAKING

SSB may occur in systems where the equations describing the system have > < a SYMMETRY which is NOT (T-Tc) 0 (T-Tc) 0 OBEYED by the GROUND STATE

Consider a ferromagnet at temperatures above and below the Curie point:

Spins randomly oriented Spins aligned Rotational Symmetry Rotational symmetry broken Electroweak Unification

In the Standard Model SSB is introduced ‘by hand’ by introducing new fields (4 degrees of freedom)

2 2 And and interaction potential V ( µ , λ ) with µ analogous to T-Tc

Choosing µ 2 < 0 ⇒ Spontaneous Symmetry Breaking

The 4 degrees of freedom

• three masses (one each for W+, W-, Z0) • One physical spin-0 (scalar) particle (the Higgs Boson) The mass of the Higgs boson is NOT predicted by the theory M 2 The masses of the W and Z are related by the weak-mixing angle sin 2 ϑ = 1− Z W 2 M W The W and Z bosons were both discovered at CERN in 1984 (at the predicted masses) !

Design and construction of the Large Electron Positron Collider at CERN The LEP e + e − Collider at CERN

LAKE GENEVA GENEVA POINT 8. CERN POINT 2. Two phase experimental

CERN Prévessin program planned:

POINT 6. POINT 4.

DELPHI

L3

SPS

e - Electron e + Positron

OPAL

ALEPH LEP

s

R. Lewi jan. 1990

0 Phase 1 - precision measurements of the Z (Ecm= MZ) completed

Phase 2 – precision measurements of the W (Ecm > 2MW) ends soon (Sept/2000) Most recent running has been at energies up to 209 GeV The OPAL Detector at LEP

Electromagnetic calorimeters Run:event 4093: 1000 Date 930527 Time 20716 C t rk( N = 3 9 S u m p = 7 3.3 ) E ca l (N = 2 5 SumE= 32.6) Hcal(N=22 SumE= 22.6) Muon detectors Ebeam 45.658 Evis 99.9 Emiss -8.6 Vtx ( -0.07, 0.06, -0.80) M u o n (N = 0 ) S ec Vtx(N= 3) Fdet(N= 0 SumE= 0.0) Bz=4.350 Thrust=0.9873 Apl an=0.0017 Obl at=0.0248 Spher=0.0073 Hadron calorimeters and return yoke

Jet chamber

Vertex detector

Microvertex detector

y Y

Z chambers θ ϕ X Z Solenoid and Pressure Vessel z x 200. cm. 5 10 20 5 0 Ge V Presamplers Cen t r e o f s c r een i s ( 0 . 0000 , 0 . 0000 , 0 . 0000 )

Original forward detector Time of flight detector

Silicon-tungsten forward detector

e +e − → Z 0 → qq → hadron jets Some Basic Collider Physics

How does one calculate the rate for some physics process at a collider ?

M = sum of all contributing processes (diagrams) – here for e +e − → W + W −

e- W- e- W- e- W- γ 0 Z ν + ..... ++e

e+ W+ e+ W+ e+ W+

Define CROSS-SECTION σ ∝ | M | 2 (units of length2)

~ cross-sectional + − f •n • N e • N e size of the beams Define LUMINOSITY L ∝ bunch A

• Instantaneous production rate N = L σ • Size of data samples typically quoted in ∫ L dt (pb-1) • Number of events in data sample given by N = σ ∫L dt Standard Model Electroweak Summary

The Standard Model is very healthy (unfortunately ?)

80.6 6 ν theory uncertainty LEP1, SLD, N Data (5) − ∆α = Higgs mass from EW fit LEP2, pp Data had 0.02804±0.00065 % 80.5 68 CL 0.02784±0.00026 SMfit ] 4 M Higgs < 170 GeV @95% CL 2 GeV

[ 80.4 ∆χ

W m 2 LEP direct search limit 80.3

[ ] SM mH GeV M Higgs > 113.3 GeV @95% CL 113 300 1000 Preliminary Excluded Preliminary 80.2 0 2 3 130 150 170 190 210 10 10 10 [ ] [ ] mt GeV mH GeV

Electroweak quantities affected by virtual particle loops

e- f e- f t Z M 2 ZZ ZZ sin 2 1 Z ϑW = − 2 M W t- - H - e+ f e+ f 2 (Mt/MW) ln(MH/MW) The SM Does Not Do Everything Some examples: Quarks and leptons are unrelated fundamental What causes the hierarchy in the fermion fermions, yet their electric charges are related masses ? (these are free parameters in the by simple ratios. Why should this be the case ? SM) particle ν d u e Mu,d ~ 0.3 GeV Æ Mt ~ 170 GeV | Q | 0 1 2 1 3 3

What causes electroweak symmetry breaking ? (Higgs mechanism for SSB put in by hand)

GRAND UNIFIED THEORIES attempt to provide answers by postulating that the strong and electroweak forces unify to a single force at some high energy scale (MGUT)

¾ there is a single force with coupling α GUT ¾ quarks and leptons are related ⎛ e − ⎞ The structure of the theory requires that ⎜ ⎟ the charge in this multiplet sum to 0 ⎜ν e ⎟ e − ⎛ ⎞ Q(ν ) + Q(e ) + 3Q(d) = 0 instead of ⎜ ⎟ we get ⎜ d ⎟ e ⎜ν ⎟ ⎜ r ⎟ ⎝ e ⎠ SUCCESS ! But there ⎜ dg ⎟ ⎜ ⎟ are problems too Colour indices: red, green, blue ⎝db ⎠ Running of Coupling Strengths Imagine measuring the electromagetic coupling strength via ee scattering α

ff q = + ff+ + .... ff α Charge Screening – the observed charge depends on the energy scale

quark confinement e- + - Asymptotic freedom e- e e e+ e+ - e- e+ e+ e- electromagnetic interaction (charge screening) e f α strong coupling + + γγ e e - e- e+ e weak coupling - f e electromagnetic coupling

- - e e strong interaction(colour anti-screening) momentum transfer Q q γ gg ∼ 1 distance scale q + + Q e e + g gg 2 g momentum transfer q Some GUT Problems

For a single force with a single coupling at MGUT expect α1 = α 2 = α 3

60 µ ( ) U(1) E.M. Force 0 + -1

α τ (p → π e ) 50 α-1 ( µ ) 1 u 0 40 π SU(2) Weak Force u Grand Unified# 30 α-1 ( µ ) u 2 (GUT) Scale + 20 SU(3) Strong Force d e α-1 ( µ ) 3 10 No Supersymmetry (+ other diagrams)

0 Inverse coupling constant Inverse coupling constant 103 105 107 109 1011 1013 1015 1017 Energy Scale, µ [GeV]

Quark-lepton relationship proton decay Simplest models predict τ ( p → π 0 e + ) ~ 10 28 − 1031 years

Inconsistent with experimental results τ (p → π 0e+ ) > 4.4×1033 years @ 90%CL

( from SuperKamiokande) The Naturalness Problem

Masses in SM get radiative corrections Mphysical = M0 +δM

Naturalness (aesthetic criterion) requires O(Mphysical ) ≈ O(M0 ) ≈ O(δM) i.e. no fine tuning

2 2 This is not true for fundamental scalars (Higgs) for which (δM) ∝ Λ

where Λ is the highest energy to which the theory remains valid

So for MH < 1 TeV (SM bias) require either Λ ≈1TeV i.e. SM breaks down at 1 TeV, OR

Some symmetry exists which can produces

O(δM) ≈ O(M H ) independent of Λ

Such a symmetry exists Supersymmetry Supersymmetry Each SM boson (fermion) has a fermionic (bosonic) supersymmetric partner with IDENTICAL MASS and Standard Model COUPLINGS ~ W ± W ± leptons sleptons 0 ~ 0 gauginos ⎛ e ⎞ ⎛ µ ⎞ ⎛ τ ⎞ ⎛ ~e ⎞ ⎛ µ~ ⎞ ⎛ τ~ ⎞ Z Z ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ↔ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ~ ⎜ ⎟ ⎜ν ⎟ ⎜ ⎟ ⎜ ~ ⎟ ⎜ν~ ⎟ ⎜ ~ ⎟ γ γ ⎝ν e ⎠ ⎝ µ ⎠ ⎝ν τ ⎠ ⎝ν e ⎠ ⎝ µ ⎠ ⎝ν τ ⎠ ~ 0 ~ 0 u c t u~ ~c t h h ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ~ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ↔ ⎜~⎟ ⎜~⎟ ⎜~⎟ H 0 H 0 higgsinos ⎝d⎠ ⎝s⎠ ⎝b⎠ ⎝d⎠ ⎝ s ⎠ ⎝b⎠ 0 ~ 0 quarks squarks A A ~ H ± H ± g ~g gluinos

This defines the particle content of the Mass eigenstates are mixtures of Minimal Supersymmetric Standard Model gauginos and higgsinos or MSSM ~ ± 2 Charginos χ i=1,2 ~ 0 4 Neutralinos χ j=1,4 Supersymmetry is a Broken Symmetry

Supersymmetry requires a doubling of the particle spectrum. Is this cost excessive ? It has been successful before (anti-matter) BUT

~ Me+ = Me− Me ≠ M e

We do not see supersymmetric matter made of snucleons and selectrons

Supersymmetry is a BROKEN SYMMETRY

But …. If supersymmetry is to solve the NATURALNESS PROBLEM, we require

MSUSY ≤ 1 TeV

This is often referred to as WEAK-SCALE SUPERSYMMETRY R-parity

R-Parity is a quantum number which distinguishes SM and supersymmetric particles

R = (−1)3(B−L)+2S Most supersymmetric models assume R-Parity Conservation This has two important consequences:

• Supersymmetric particles must be produced in pairs • There must be some Lightest Supersymmetric Particle or LSP

~0 This LSP is usually the lightest neutralino χ1 and is a good Cold Dark Matter candidate or WIMP (Weakly Interacting Massive Particle) Coupling Constant Evolution - SUSY Force unification revisited (now with MSSM particle content)

60 µ

( ) U(1) E.M. Force -1 α 50 p → K +ν α-1 ( µ ) 1 40 Grand Unified# u u + SU(2) Weak Force (GUT) Scale K 30 α-1 ( µ ) s 2 ? u 20 SU(3) Strong Force α-1 ( µ ) ν 10 3 With Supersymmetry d

0 Inverse coupling constant Inverse coupling constant 103 105 107 109 1011 1013 1015 1017 Energy Scale, µ [GeV] We still have a quark-lepton 0 + 38±1 relationship and therefore proton in SUSY GUTs τ (p → π e ) = 10 years decay. Dominant mode in SUSY GUTs is p → K +ν

Model predictions vary: τ ( p → K + ν ) ~ 10 30 − 10 36 years Experimental limits τ ( p → K + ν ) > 1 . 9 × 10 33 years @ 95% CL (Super K)

Super Kamiokande detector will probe lifetimes up to 1034 years Supersymmetric Model Parameters

MSSM has 105 free parameters ( in addition to the 19 free parameters of the SM) !!!

• masses • couplings • mixing angles • other parameters arising from supersymmetry breaking

Frequently results of supersymmetric particle searches are interpreted within the framework of the Constrained MSSM which assumes that many free paramters of the MSSM unify at the GUT scale

5 parameter Constrained MSSM Other Features of Supersymmetric GUTS

• Unification of free parameters at the GUT scale (as for the couplings)

2 • Can provide a correct prediction of sin ϑ W (experimentally 0.2198 +/- .0021)

• Mechanismm for Electroweak symmetry breaking: ¾ µ 2 positive at the GUT scale but ‘runs’ negative at the EW scale

• Mass prediction for the lightest higgs ! ¾ M(h0) < 130 GeV (MSSM) ¾ M(h0) < 150 GeV (Supersymmetry in general)

•May allow for unification with gravity: ¾ Most string theories are supersymmetric Sensitivity to New-Particle Production

REQUIREMENTS for DIRECT OBSERVATION of a particle X with mass MX

• X production (some process) must be kinematically accessible • the production process must have σ > ( ∫ L dt ) − 1

ECM > 2M X ¾ for instance for e+e− → XX ( L dt)−1 > 10 pb−1 if σ ( e + e − → XX ) = 0 . 1 pb require } ∫

NON-OBSERVATION of a PROCESS implies only that the CROSS-SECTION is lower than the sensitivity of the data sample

One can EXCLUDE A MODEL if it predicts a cross-section that is excluded

One can EXCLUDE THE EXISTENCE OF PARTICLE X only if the cross-section (at a given energy) is a function of the mass only or if other relevant parameters are scanned

CROSS-SECTION LIMITS are typically ~ model independent (measurements)

MASS LIMITS are typically model dependent (interpretations of measurements) Supersymmetric Particle Searches at LEP

LEP is an electroweak machine Best candidates for SUSY searches are the lowest mass charginos and neutralinos + − ~0 ~0 e e → χ1 χ1 invisible

+ − ~ + ~ − Best discovery channel at LEP e e → χ1 χ1

- - - e χ˜ 1 e - χ˜ 1 σ(e+e-→W+W-) γ,Z + ν˜ 10 e

+ + + χ˜+ e χ˜ 1 e 1 ) (pb) -

1 1 χ 1 + processes interfere destructively χ OPAL sensitivity →

-

e -1 + 10 (e σ M > 45 GeV ν˜ E = 183 GeV M ν˜ > 200 GeV (minimum σ) cm -2 10 50 60 70 80 90 100 ± χ1 mass [GeV] Chargino Decays – Experimental Signatures

l, q 1 l,ν q ± W ˜ ν˜ ± q˜ χ˜ ν ± l, χ˜ 0 1 , q2 χ˜ χ˜ 0 1 χ˜ (missing energy) Decay Mode 1 1 (missing energy) 1

˜ 0 ν q χ1 (missing energy) ,l

Experimental lepton + missing energy lepton + missing energy hadron jets + missing energy Signature hadron jets + missing energy

~0 χ1 is massive and interacts only weakly with matter (i.e. the detector) carries off missing (undetected) energy

+ − ~ + ~ − So for e e → χ 1 χ 1 experimental signatures are: Experimental Signature SM background jets + missing energy e+e− → ZZ → (qq)(νν ) jets + leptons + missing energy e+e− → W+ W− → (qq′)(lν ) 2 leptons + missing energy e+e− → W+ W− → (lν )(l′ν ) Missing energy is carried off by neutrinos Experimental Signatures Cont’d

So what do these events look like in the detector ?

jets + missing energy jet + lepton + missing energy 2 leptons + missing energy

Look for an excess of such events over expected SM background A Chargino Candidate Event

Ru n : 7445 D a t e : 13 . 0 8 . 1996 B e am En e r gy : 8 0.5 G eV E v en t : 28219 T im e : 14 : 5 6 . 4 2 h

Si d e v i ew - p l a n e o f T hru s t a x i s y P h i = 183 . jets + missing energy channel

z Also consistent with Ph i = 9 3 . coming from a SM process:

x z Si d e v i ew - p l a n e p erp . t o T hru s t x-y v i ew e+ q 2 2 1/ 2 M = (E − P ) ~ M Z* q miss miss miss Z ν Z ν e- Missing energy carried off by neutrinos ? ν Cross-section Limits

Signal for new physics is an excess of events above the SM backgrounds But ….

Nevents(selected) consistent with Nevents(expected from SM processes) + − ~ + ~ − Place limits on σ (e e → χ1 χ1 ) ~0 ~ ± OPAL in plane of M ( χ 1 ) vs M(χ1 )

90 (a) [0.2 pb, 0.4 pb] [0.09 pb, 0.12 pb]

) [GeV] 80

0 1 [0.12 pb, 0.2 pb] ~ χ [0.075 pb, 0.09 pb] 70 m( [0.068 pb, 0.075 pb] 60 50 [0.09 pb, 0.12 pb]

40 [0.12 pb, 0.2 pb] These results are at 30 Ecm = 189 GeV 20 [0.2 pb, 0.4 pb] 10 [0.4 pb, 0.75 pb] [0.75 pb, 1.37 pb] 0 50 60 70 80 90 χ~± m( 1) [GeV] Mass Limits for Supersymmetric Particles

Model dependent mass limits can be set by scanning the CMSSM parameter space and comparing predicted cross-sections with experimental limits

Mass limit for MSSS Cold Dark Experimental σ Limits MSSM Parameter space + - + - σ(e e → χ˜˜1 χ1) 5 Free parameters Matter Candidate + - 0 0 σ(e e → χ˜˜2 χ1) etc OPAL Vary some or all 60 MSSM parameters 50 [GeV] ) 0 1 40 ~ χ ( 30 All masses, BRs, σ etc m 31.6 GeV Excluded 20 fully determined at 95% CL 10 0 1 2 345 10 20 30 40 ? Parameter set excluded tan β

last scan parameter

0 M(˜χ0) (for instance) χ˜1 mass limit 1 Excluded for all parameters ? ~0 M(χ1 ) > 31.6 GeV @95% CL Dark Matter

Matter whose existence has been inferred only via its gravitational effects There is extensive evidence that much of this is non-baryonic weakly interacting particles ¾ hot dark matter (relativistic) e.g. neutrinos ¾ cold dark matter (non-relativistic)

Weakly ~0 Interacting χ1 is an excellent CDM candidate in Massive } most of the MSSM parameter space Particles S Strong evidence comes from the rotation curves of spiral galaxies 1 Expect v ( r ) ∝ Observe v(r) ~ independent of r r This FLAT ROATATION CURVE implies that M ∝ r This is the expected mass profile of a self gravitating ball of ideal gas at a uniform temperature Direct Dark Matter Searches

In the early universe e+e− → XX Production WIMP number density in equilibrium with + − − + For T>>TX XX → e e Annihilation e ,e ,γ

For T < TX the WIMP number density drops until the mean free path for annihilation exceeds the size of the universe hep-ex/9709019 19Sep1997 RELIC ABUNDANCE Cold finger 21g LiF Cross-section for elastic scattering of a WIMP off a NTD thermistor nucleus calculable with specific models Au wire Can do direct searches for WIMPS

WIMP

Apparatus at 10 mK Requires proper shielding Cu ribbon Spring contact 1cm Collimator bolometer Dark Matter – Experimental Summary

10000 Tokyo LiF detector will reach Tokyo(LiF) WIMP-p cross-section of 0.01pb 1000 surface EDELWEISS(sapphire) 4800m.w.e.

100 BPRS(CaF2(Eu)) 3500m.w.e.

10 UKDMC(NaI(Tl)) UPDATE: 3600m.w.e. Lots of experiments, including 1 Excluded by OPAL Canadian experiement PICASSO at 95% CL (heavy sfermions, WIMP-p cross section[pb] 0.1 m0 = 200 GeV)

0.01 MSSM OPAL limit indicated is somewhat dated

0.001 1 10 100 1000 10000 WIMP Mass[GeV] The LHC pp Collider at CERN

14 TeV pp collider to be installed in the existing LEP ring First collisions scheduled for 2005 Two general purpose detectors approved for LHC ATLAS (+ Canada) and CMS

Main objectives: Discover the new TeV scale physics ¾ Discovery of the Higgs ¾ Discover of Weak-Scale SUSY or fully exclude it

The LHC is a strong-interaction machine SUSY production rates will be highest for q~ and ~g

LHC Low-luminosity running 104 pb-1 / year (3 years) LHC High-luminosity running 105 pb-1 / year (3+ years)

cross-sections for supersymmetric particle production can be enormous ! 102 –103 pb (recall N = σ ∫ L dt ) New Particle Searches at Hadron Colliders

Hadon Colliders can achieve higher centre-of-mass energies than electron-positron machines ….. BUT

ECM of constituent collision ≠ 2×Ebeam proton remnant p Ebeam Ebeam uu q q pp p g q q d p

3 valence quarks + ‘sea’ quarks + gluons proton remnant

1 0.9 Gluons carry ~ 50% of the protons momentum 0.8 0.7 Collision is between two particles each 0.6 carrying some fraction x of the protons 0.5 u momentum 0.4 d 0.3 effective 0.2 0 < x < 1 ⇒ 0 < ECM < 2Ebeam 0.1 u d s 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 momentum fraction x Supersymmetric Particle Production at LHC

-1 p LHC will discover (with 10 pb ): q ~ ~ q˜ ~~ ¾ g and q up to ~ 2 TeV g˜ qq q q˜ ~ ¾ l , χ~0 , χ~ ± over a more restricted range p j i

σ(pb) pp collisions at E = 14 TeV p cm q g˜ q˜ q~~g g q˜ Mq=2Mg Mq=Mg p sum(qq˜˜ + qg˜˜ + gg)˜˜

χ˜˜+ χ- p 1 1 g g˜ ~~ g˜ gg g g˜ p [ ] gluino mass Mg˜ GeV Conclusions

General arguments NEED FOR PHYSICS BEYOND THE SM

Some of these arguments NEW PHYSICS AT THE TeV SCALE

SUPERSYMMETRY is a serious candidate for the description of this new physics

WEAK SCALE SUPERSYMMETRY (relevant to the naturalness problem) might be accessible at current colliders. If not, it will be DISCOVERED OR EXCLUDED by the LHC experiments The Latest Theoretical Vogue: Large Extra Dimensions

−17 • Hierarchy problem: MEW / Mplanck ≈10

• Postulate Mplanck effective energy scale, not fundamental • Assume n compact spatial dimensions of (compactified) radius R m m 1 V()r = 1 2 • (r << R) 2+n n+1 Effective 4-dimensional Mplanck then given by M D r (30/n)-17 Requiring MD ~ MEW Æ R ~ 10 cm ⎧m1m2 1 ⎫1 (r >> R) 13 V()r = ⎨ n+2 • n ⎬ n=1 Æ R ~ 10 cm - ⎩ M D R ⎭r excluded by 1/r2 tests of

Short-range gravity with Large Compact Extra Dimensions gravity 10 11

10 8 n=2 Æ R ~0.1-1mm - n = 4 10 5 limited to very high M by relative strength n = 3 D 10 2 n = 2 SN1987 data -1 n = 1 10

-4 10

-7 10 There are other models with infinite sized -10 10

-13 10 extra dimensions (non-factorizable space-

-16 10 time geometry) for which n=1 is not excluded -19 2 10 1/r -22 10 -2 -1 2 3 4 5 6 7 8 9 10 11 10 10 1 10 10 10 10 10 10 10 10 10 10 10 distance (cm)