dimensions at dØsearch for large extra€¦ · fermilab w&c, 4/21/2000 greg landsberg,...

Search For Large Extra Dimensions at DØ

Greg Landsberg

(for the DØ Collaboration)Fermilab Wine & Cheese Seminar

April 21, 2000

Fermilab W&C, 4/21/2000 Greg Landsberg, Searches for Large Extra Dimensions at D0

OutlineTheory of Large Extra DimensionsCurrent Limits on Large Extra Dimensions

Cosmological ConstraintsGravity at Short DistancesLEP2 Searches for Extra Dimensions

Direct Graviton EmissionVirtual Graviton Effects

DØ Run I Search for Virtual Graviton EffectsMethodData SelectionResults

Projections for Run II and Future CollidersUnusual Signatures for Extra Dimensions (Black Holes)Conclusions


Life With the Standard Model

is boringly precise: but not at all boring:Standard Model accommodates, but does not explain:

EWSBCP-violationFermion masses

Higgs self-coupling is positive, which leads to a triviality problem that bounds mH from aboveThe natural mH value is Λ, where Λ is the scale of new physics; if SM is the ultimate theory up to GUT scale, an extremely precise (∼ (v/mGUT)2) fine-tuning is required

v MGUT MPl

GravitationalForce

E [GeV]

EM/HyperchargeForce

Weak Force

Strong Force

Inve

rse

Stre

ngth

RGE equations

1016102 1019

Measurement Pull Pull-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

mZ [GeV]mZ [GeV] 91.1871 ± 0.0021 .07

ΓZ [GeV]ΓZ [GeV] 2.4944 ± 0.0024 -.62

σhadr [nb]σ0 41.544 ± 0.037 1.72

ReRe 20.768 ± 0.024 1.19

AfbA0,e 0.01701 ± 0.00095 .70

AeAe 0.1483 ± 0.0051 .13

AτAτ 0.1425 ± 0.0044 -1.16

sin2θeffsin2θlept 0.2321 ± 0.0010 .65

mW [GeV]mW [GeV] 80.401 ± 0.048 .15

RbRb 0.21642 ± 0.00073 .85

RcRc 0.1674 ± 0.0038 -1.27

AfbA0,b 0.0988 ± 0.0020 -2.34

AfbA0,c 0.0692 ± 0.0037 -1.29

AbAb 0.911 ± 0.025 -.95

AcAc 0.630 ± 0.026 -1.47

sin2θeffsin2θlept 0.23096 ± 0.00026 -1.87

sin2θWsin2θW 0.2255 ± 0.0021 1.17

mW [GeV]mW [GeV] 80.448 ± 0.062 .88

mt [GeV]mt [GeV] 174.3 ± 5.1 .11

∆αhad(mZ)∆α(5) 0.02804 ± 0.00065 -.20

Moriond 2000

MH

[GeV

/c2]

600

400

500

100

200

300

03 5 7 9 11 13 15 17 19

log10 Λ [GeV]

Triviality

EW vacuum is absolute minimum

EWPrecision

Direct

MH < 188 GeV @ 95% CL(Combined EW fit)

MH > 107.9 GeV @ 95% CL(LEP2, up to 202 GeV)


Life Beyond the Standard Model

We conclude that the SM is just an effective theory, a low-energy approximation of a more complete model that explains things postulated in the SMThis new theory takes over at the scale Λ, comparable with the Higgs mass, i.e. Λ ∼ 1 TeVTwo main candidates for such a theory are:

SUSY (SUGRA, GMSB, AMSB)Strong Dynamics (TC, ETS, topcolor, top see-saw, )

But: what if there is no other scale, and the SM model is correct up to the Planck scale?

Arkani-Hamed, Dimopoulos, Dvali (ADD) (1998): what if the Planck scale is ∼ 1 TeV?!!Low energy GUT unification is also possible with extra dimensions: Dienes, Dudas, Ghergetta (1998)

MZ MGUT

MPl

MS MGUT

GravitationalForce

logE

EM/HyperchargeForce

Weak Force

Strong Force

Real GUT Scale

VirtualImage

Inve

rse

Stre

ngth

MPl


Crazy Idea? But it Works!

What about Newtons law?

Ruled out for flat extra dimensions, but has not been ruled out for sufficiently small compactified extra dimensions:

Flat Dimension

Com

pact

Dim

ensi

on

( ) [ ]( ) 121

23

212

11+++

→=nnn

PlPl rmm

Mrmm

MrV

( ) [ ]( ) RrrR

mm

MrV

nnnPl

>>∝ ++for

1 2123

MS effective Planck Scale

But: how to make gravity strong?GN = 1/MS

2 ∼ GF ! MS ∼ 1 TeV

More precisely, from Gausss law:

Amazing as it is, but no one has tested Newtons law to distances less than ∼ 1mmTherefore, large spatial extra dimensions compactified at a sub-millimeter scale are, in principle, allowed!

nPl

nS RMM 22 ∝+

""#

""$

%

=×===×

∝&&'

())*

+π

=

− 4106

33

27.0

1108

2

1

12

12

2

n,m

n,nm

n,mm

n,m

M

M

MR

n/

S

Pl

S


Examples of Compactified Spatial Dimensions

M.C.Escher, Mobius Strip II (1963) M.C.Escher, Relativity (1953)[All M.C. Escher works and texts copyright © Cordon Art B.V., P.O. Box 101, 3740 AC The Netherlands. Used by permission.]


An Importance of Being Compact

Compactified dimensions offer a way to increase tremendously gravitational interaction due to a large number of the available winding modesThis tower of excitations is known as Kaluza-Klein modes, and such gravitons propagating in the compactified extra dimensions are called Kaluza-Klein gravitons, GKK

From the point of view of a 3+1-dimensional space time, the Kaluza-Klein graviton modes are massive, with the mass per excitation more ∼ 1/RSince the mass per excitation mode is so small (e.g. 400 eV for n = 3, or 0.2 MeV for n = 4), a very large number of modes can be excited at high energies

Compactifieddimension

R

GKK

Flat dimension

( ) ( ) !2102 , ,,kkRxx =π+φ=φ

M(GKK) = √Px2 = 2πk/R

Each Kaluza-Klein graviton mode couples with the gravitational strength For a large number of modes, accessible at high energies, gravitational coupling is therefore enhanced drasticallyLow energy precision measurementsare not sensitive to the ADD effects


Phenomenology of Large Extra Dimensions

New idea, inspired by the string theory, with direct connection to the observables

Since large extra dimensions bring the GUT and gravity scales right at the EWSB scale, they solve the hierarchy problemThere are multiple mechanisms that allow gauge fields in the bulk to communicate symmetry breaking to our brane

A new mechanism, shining is a powerful way of introducing a small parameter into the theory, and explain many yet unsolved phenomena, such as CP violation, etc.New framework, possibly explaining neutrino masses, EWSB mechanism, and other puzzling phenomenaFirst alternative to the established EWSB candidates in 25 years! What took us so long?A significant theoretical interest to the subject ensures rapid development of this fieldOver 150 theoretical papers on this subject over the past two years truly a topic du jour

SM

bulk

gaugefields

via gravity

bulk

big bang

CP-

bran

eshining

SM


Cosmological Limits on Large Extra Dimensions

Supernova cooling due to the graviton emission

Any new cooling mechanismwould decrease the thought-to-be dominant cooling by the neutrino emissionTightest limits on any additional cooling sources come from the measurement of the SN1987A neutrino flux by the Kamiokande and IMBApplication to the ADD scenario [Cullen, Perelstein, PRL 83, 268 (1999)]:

MS > 30 TeV (n=2)MS > 4 TeV (n=3)

Distortion of the cosmic diffuse gamma radiation (CDG) spectrum due to the GKK → γγdecays

Best CDG measurement come from the COMPTEL instrument in the 800 KeV - 30 MeV range Application to the ADD scenario [Hall, Smith, PRD 60, 085008 (1999)]:

MS > 100 TeV (n=2)MS > 5 TeV (n=3)

Caveat: there are many known (and unknown!) uncertainties, so the cosmological bounds are reliable only as an order of magnitude estimateStill, n=2 seems to be excluded


Current Limits from Gravitational Experiments

1798: Cavendish experiment (torsion balance)

Mid-1970-ies: a number of Cavendish-type experiments searching for the fifth forth via deviations from Newtons lawSensitivity vanishes quickly for distances less than 1 mmMajor background: Van der Waals and Casimirforces

Status of short-range gravity experiments

Best sub-millimeter results are from 1997 Lamoreaux experiment [PRL 78, 5 (1997)] to measure the Casimir forceSensitivity is many orders of magnitude lower than needed to test ADD theory

Down Modulus

10

10

10

10

10-6

10-5

10-4

10-3

10-2

8

4

0

-4

λ (meters)

α

Excluded

Region

String Dilaton

Axion

Strange Modulus

Gluon Modulus

Experiment

Lamoreaux

Mitrofanov, et. al.

Irvine

Radius Modulus

Vacuum energy constraints with

(40 < H < 90) km/s Mpc -10

ProposedADD model

Mitrofanov

Irvine

Lamoreaux[From Long/Chan/Price hep-ph/9805217]


New Generation of Gravitational Experiments

New generation of precision experiments to measure gravity at short distances (100 µm or less) is being built:

Long/Chan/Price @ ColoradoKapitulnik/Kenny @ Stanford

Colorado setup:Use low temperatures and SQUID resonance pickup (∼ 1 KHz) to increase the sensitivity and diminish seismic and vibrational effectsGold-foil shield against the Van der Waals force(Casimir force is small for distances > 1 µm)Plan to measure gravity at the distances between 100 µm and 1 mm; to a precision necessary to test the ADD modelFuture LHe experiment will be able to probe gravity at even shorter distances ∼ 10 µm

First results from both experiments are expected this Spring; will be able to test n=2, but can not probe higher number of dimensionsOne needs particle accelerators to probe gravity at sub-micrometer distances

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Vibrating Reed(Source Mass)

Sapphire Shield

Detector Oscillator

VibrationIsolation Stack

1 cm

AAAAAAAAAAAAA

CapacitiveTransducer

TorsionAxis

AA

a)

b)

d

Detector (Oscillator)

Shield

Source Mass Positions

t d

t s

Torsion Axis

dmin

max

R

Long/Chan/Price setup


Collider Signatures for Large Extra Dimensions

Kaluza-Klein gravitons couple to the momentum tensor, and therefore contribute to most of the SM processesFor Feynman rules for GKK see:

Han, Lykken, Zhang, PR D59, 105006 (1999)Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999)

Since graviton can propagate in the bulk, energy and momentum are not conservedin the GKK emission from the point of view of our 3+1 space-timeSince the spin 2 graviton in generally has a bulk momentum component, its spin from the point of view of our brane can appear as 0, 1, or 2Depending on whether the GKK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing ET or fermion/vector boson pair production

Real Graviton EmissionMonojets at hadron colliders

GKK

gq

q GKK

gg

g

Single VB at hadron or e+e- colliders

GKK

GKK

GKKGKK

V

VV V

Virtual Graviton Emission Fermion or VB pairs at hadron or e+e- colliders

V

V

GKKGKK

f

ff

f


LEP2 Searches for Direct Graviton Emission - I

e++++e−−−− →→→→ γγγγGKKPhoton + MET signatureRecycling of the GMSB analysesALEPH (2D-fit), DELPHI, L3 (x)

1

10

10 2

10 3

10 4

400 600 800 1000 1200 1400 1600 1800 2000

M D > 1250 GeV for n=2M D > 792 GeV for n=4

n=2

n=4

M D (GeV)

σ (f

b)

196+200+202 GeV(202 pb-1)

HPC+FEMC acceptance

DELPHI

95% limitσ95 = 0.17 pb

( ) ( )

( ) ( )( ) ( ) ( ) ( )[ ]442222

2

1

2

2

2

13121

12,

cos,2

,,32

2

2

zxzxxxxxzx

xzxf

zs

Exzxf

M

s

sdxdz

d

n

n n

Sn

−−−+−−−−=

θ==&&'

())*

+Γπα=σ

−

γ

+

Theory:[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version: hep-ph/9811291]Experiment:ALEPH-CONF-2000-005DELPHI 2000 CONF 344L3: Phys. Lett. B470, 268 (1999)

0

25

50

75

100

0 20 40 60 80 100 120 140 160 180

Missing Mass (GeV/c2)

Ent

ries/

(3 G

eV/c2 ) ALEPH

√s = 161-189 GeV(a)

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

|CosΘ|

Ent

ries/

0.05

(b)

MS = 1 TeV, n=2

MS = 1 TeV, n=2ALEPH, 99 DELPHI, 00

Results:MS > 1.3-0.6 TeVfor n=2-6 (DELPHI)ALEPH, L3 slightlyworse

Z(νν) background


LEP2 Searches for Direct Graviton Emission - II

e++++e−−−− →→→→ ΖGKKZ(jj) + MET signature

Recycling of the invisible Higgs analyses

ALEPH: Z(jj)G, 184 GeV, total cross section method

L3: Z(jj)G, 189 GeV, increased sensitivity via analysis of the visible mass distribution

MS > 0.35-0.12 TeV (ALEPH)for n = 2-6

MS > 0.60-0.21 TeV (L3)for n = 2-6

( )( ) ( )

( )( )( )

( ) ( ) xyyxAx

AAxydydxI

IM

M

nZ

GZ

x

n

n

S

Z

nn

41,16

12

231

41

ffff

21

0

1

0 22

2

2 22

22

−−−=−+

Γπ=

&&'

())*

++π

=→Γ→Γ

, ,−

+

−−

Theory:[Balazs, Dicus, He, Repko, Yuan, Phys. Rev. Lett. 83, 2112 (1999) width ratio][Cheung, Keung, Phys. Rev. D60, 112003 (1999) mass distribution]

Experiment:ALEPH-CONF-99-027L3: Phys. Lett. B470, 281 (1999)

MS = 0.5 TeV, n=2

≤≤≤≤189 GeV


Virtual Graviton EffectsIn the case of pair production via virtual graviton, gravity effects interfere with the SM (e.g., l+l- at hadron colliders):

Therefore, production cross section has three terms: SM, interference, and direct gravity effectsThe sum in KK states is divergent in the effective theory, so in order to calculate the cross sections, an explicit cut-off is requiredAn expected value of the cut-off is ≈ MS, as this is the scale at which the effective theory breaks down, and the string theory needs to be used to calculate production

Unfortunately, a number of similar paperscalculating the virtual graviton effects appeared simultaneouslyHence, there are three major conventionson how to write the effective Lagrangian:

Hewett, Phys. Rev. Lett. 82, 4765 (1999)Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999); revised version, hep-ph/9811291Han, Lykken, Zhang, Phys. Rev. D59, 105006 (1999); revised version, hep-ph/9811350

Fortunately (after a lot of discussions and revisions) all three conventions turned out to be completely equivalent and only the definitions of MS are different:

s

qq `

`+

; Z

+

qq `

`+

Gn

2+

gg `

`+

Gn

2

( ) ( ) ( ) ( )M,cosfM

nbM,cosf

M

nadMcosd

d

dMcosd

d

*

S

*

S

*SM

*

θ+θ

+θσ=

θσ

2814

22


Hewett, GRW, and HLZ Formalisms

Hewett: neither sign of the interference nor the dependence on the number of extra dimensions is known; therefore the interference term is ~λ/MS

4(Hewett), where λ is of order 1; numerically uses λ = ±1GRW: sign of the interference is fixed, but the dependence on the number of extra dimensions is unknown; therefore the interference term is ~1/ΛT

4

(where ΛT is their notation for MS)HLZ: not only the sign of interference is fixed, but the n-dependence can be calculated in the effective theory; thus the interference term is ~F/MS

4(HLZ), where F reflects the dependence on the number of extra dimensions:

Correspondence between the three formalisms:

Rule of thumb:

( ) ( )GRWHewett TSM Λπ

≡+=λ

41

2

( )"#

"$%

>−

==

22

22,log

2

n,n

nsM S

F

( ) ( )HLZHewett 44 2 SS MM

Fπ=λ

( ) ( )HLZGRW 4

1

ST M

F=Λ

( ) ( )51 ==λ

≈nSS MM HLZHewett

( ) ( )4=

=ΛnST M HLZGRW


0

1

2

3

4

5

0 0.2 0.4 0.6 0.80

10

20

30

40

cos(θ∗ )

dσ ⁄

dΩ [p

b ⁄ s

r]

Eve

nts

OPAL preliminary

e+e− γγ(γ)202 GeV

LEP2 Searches for Virtual Graviton Effects

LEP2 Collaborations looked at difermionand diboson production due to the GKKexchangeUnfortunately, different formalisms were used by different collaborations, and sometimes even within a collaboration, which makes results hard to compare and combineInternal inconsistency could affect some of the combined limits Most sensitive channels are:

Dielectron s-channel production and Bhabha scatteringDiphoton production

Limits on MS(Hewett) ~ 0.8-1.0 TeVBibliography:

ALEPH: CONF 99-027, 2000-005DELPHI: CONF 355, 363 (2000)L3: PL B464, 135; B470, 281 (1999)OPAL: CERN-EP/99-097, PN 420 (1999)

√s (GeV)

e+e- → e+e-L3

preliminary

DataSMMs=0.75 TeV, λ=+1Ms=0.75 TeV, λ=-1

Cro

ss S

ect

ion

(n

b)

0.01

0.02

0.03

0.04

0.05

0.060.070.08

120 140 160 180 200

L3 Note 2516 (2000)

≤≤≤≤202 GeVee

202 GeV

OPAL PN 420 (1999)

γγ

ALEPH CONF 99-027

ee

189 GeV

N.B. All LEP Collaborationsconsidered both interference signs


LEP2 Lower 95% CL MS(Hewett) Limits (TeV)

0.61 0.68

0.841.00

0.600.76

0.821.04

f f

0.61/0.68 (ff) (<189) MS for γγγγγγγγ is wrong?

0.63 0.64

0.50 0.63

0.63 0.60

OPAL

0.87/1.07 (<189) ??? 0.82/0.89 (VV)

0.76 0.77

0.68 0.79

0.80 0.79

0.49 0.49

0.580.54

0.560.69

0.910.99

L3 (???)

0.60/0.76 (ff) (<202) MS for γγγγγγγγ is wrong?

0.690.71

0.560.65

0.590.73

DELPHI

0.84/1.12 (<189) MS > 0.75/1.00

0.910.92

0.66/0.61 0.55/0.55 (bb)

0.570.59

0.630.68

0.801.03

ALEPH (ΛT)

CombinedZZWWγγγγγγγγqqττττ++++ττττ−−−−µµµµ++++µµµµ−−−−e++++e−−−−Experiment

e++++e−−−− →→→→ ZGe++++e−−−− →→→→ γγγγG

0.58

0.68

0.60

n=5

0.60

0.35

n=2

0.38

0.22

n=3

0.29

0.17

n=4

0.24

0.14

n=5

1.02

1.25

1.10

n=2

0.81

0.97

0.86

n=3

0.67

0.79

0.70

n=4

0.51

0.59

0.52

n=6

OPAL

0.21L3

DELPHI

0.12ALEPH

n=6Experiment

≤202 GeV

Color coding

λλλλ=-1 λλλλ=+1 GL

≤189 GeV

≤184 GeV

Virtual Graviton Exchange


Virtual graviton Drell-Yan and diphoton productionMass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/9904234;Cheung, Phys. Rev. D61, 015005 (2000), Phys. Lett. B460, 383 (1999),]Key improvement [Cheung, GL, hep-ph/9909218, to appear in PRD]: simultaneous analysis of the mass and angular distributions, as a spin 2 graviton would result in different angular distributions compared to the SM backgrounds; no other cuts!There are three terms: SM, interference, and direct graviton contributionUse Han/Lykken/Zhang formalism:

Virtual Graviton Exchange at the Tevatron

( )*

4cos, θ≡=η z

M S HLZF

Dileptons: Diphotons:

( )"#

"$%

>−

==

22

22,log

2

n,n

nsM S

F

( ) ( ) ( )

( )

( ) ( ) ( ) 822

42

2121

8222

4222

44

2

2

2121

2

51261

12

21

2

961

γγγγ

γγγγ

γγγγ

η++

+-.

/01

2η−π+ηπ+

−

×π+=σ

,,

3 ,,

MM

zzKxfxfdxdx

MzMQez

Qe

M

zKxfxfdxdx

dzdM

d

qg

qq

qq

q

GKK termSM

interference term

GKK term

s

qq `

`+

; Z

+

qq `

`+

Gn

2+

gg `

`+

Gn

2

[For cross section formula see hep-ph/9909218]

NLO corrections accounted for via a constant K-factor


Two-Dimensional Analysis

Parameterize cross section as a bilinear form in scale η (works for any n>2)Note the asymmetry of the interference term, σ4, for ll productionUse Bayesian fit to the data (real one or MC one) to get the best estimate of η

0 500 1000 1500 2000-1

-0.50

0.51

10-6

10-5

10-4

10-3

10-2

10-1

1

SM

M(ll), GeVcosθ

*

σ SM

, pb

0 500 1000 1500 2000-1

-0.50

0.51

-0.2

0

0.2

0.4

x 10-3

η term

M(ll), GeVcosθ

*

σ 4 ,

pb T

eV 4

0 500 1000 1500 2000-1

-0.50

0.51

10-6

10-5

10-4

η2 term

M(ll), GeVcosθ

*

σ 8 ,

pb T

eV 8

σllSM σ4

ll

σ8ll

f/MS4 Bayesian

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4

η

0 500 1000 1500 2000-1

-0.50

0.51

10-6

10-5

10-4

10-3

10-2

10-1

SM

M(γγ), GeVcosθ

*

σ SM

, pb

0 500 1000 1500 2000-1

-0.50

0.51

10-6

10-5

10-4

η term

M(γγ), GeVcosθ

*

σ 4 ,

pb T

eV 4

0 500 1000 1500 2000-1

-0.50

0.51

10-6

10-5

10-4

η2 term

M(γγ), GeVcosθ

*

σ 8 ,

pb T

eV 8

σγγSM σ4

γγ

σ8γγ

[Cheung, GL hep-ph/9909218,to appear in PRD]

284 ησ+ησ+σ=σηllllll

SMll

284 ησ+ησ+σ=σ γγγγγγγγ

η SM

[η] = TeV-4

Repeat MC experiment many times and use the median as a measure of sensitivity Sensitivity is 20-30% (in terms of ,Ldt) higher than that in 1-dimensional analysisDiphoton channel is considerably more sensitive than the dilepton one


DØ Search for Large Extra Dimensions

First designated search for extra dimensions at hadron collidersBased on Cheung/GL method with a few important modifications:

DØ detector does not have central magnetic field, so the sign of cosθ* is not measured for dielectrons ! use |cosθ*|Dimuon mass resolution at high masses is poor ! do not use dimuonsDielectron and diphoton efficiencies are moderate (~50%) due to tracking inefficiency(electrons) and conversions & random track overlap (photons) ! maximize the DØdiscovery potential by combining dielectrons and diphotons (essentially ignore tracking information), i.e. use di-EM signature!Instrumental background is not expected to be important at high masses ! open up the ID cuts to maximize the efficiency

Use EM cluster shape informationto pick the hard-scattering vertex, thus improving mass and cosθ*

resolution

10-1

1

10

10 2

100 150 200 250 300 350 400Mγγ , GeV

dσ/d

Mγγ

, fb

/GeV

dσ/dM γγ = exp(8.35-0.246Mγγ/GeV)(0.91-0.0068Mγγ/GeV+0.00018Mγγ 2/GeV2) (fb/GeV)

Total QCD

jjjγ

γγ

SM γγvs. instrumental backgrounds

[GL, Matchev, hep-ex/0001007,to appear in PRD]


Next-to-Leading Order Corrections

Angle θθθθ* in the parton level cross sections is defined as the angle between the incoming parton from p and the l+, i.e. in the Gottfried-Jackson frameIn the presence of the ISR this frame is no longer usableWe use the helicity frame instead, and define θθθθ* as the angle between the direction of the boost and the parton which follows this direction, i.e. cosθθθθ* ≥ 0ISR-induced smearing, i.e. the difference between the cosθθθθ* in the GJ and helicity frames is small (~0.05)The ISR effect is properly modeled in the signal MCSince NLO corrections for diphoton and dielectron production cross section are close, there is no theoretical overhead related to adding two channels; we use K = 1.3 ± 0.1There is no QCD FSR in the di-EM final states

boost

recoil

zISR

helicity angle

θ*

q

ql+

l-

θ* boost

z

helicity angle= GJ angle

q q

l+

l-


Data Selection and Efficiency

Use entire Run I statistics from full luminosity, low-threshold di-EM triggers, ,Ldt = 127 ± 6 pb-1

Offline cuts are determined by the availability of background triggers:

Exactly 2 EM clusters w/ ET > 45 GeV, |η|<1.1 or 1.5<|η|<2.5 passing basic IDcriteria:

EMF > 0.95ISO < 0.10χ2 < 100

MET < 25 GeVNo other kinematic cuts in the analysis, as the M/cosθ* space completely defines the process

Resulting data sample contains 1282 eventsEfficiency of the ID cuts is determined from the Z-peak data obtained with the same triggers by lowering the ET(EM) cut

10,945EM ID

1,282ET > 45 GeV

31,210Acceptance

37,146ET > 25 GeV

83,976=2 EM

84,490≥2 EM

84,509Quality cuts

86,013Starting sample

# of eventsCut

(76 ± 2)%Overall, per event

(99.4 ± 0.5)%Event quality

(99.0 ± 0.5)%MET < 25 GeV

(88 ± 2)%EM ID

EfficiencyCut


Signal and SM Background Monte Carlo

Based on Cheung/GL LO parton level generator [hep-ph/9909218] that produces weighted eventsAugmented w/ fast parametric DØdetector simulation that properly models:

DØ detector acceptance and resolutionsPrimary vertex smearing and resolutionEffects of additional vertices from multiple interactions in the eventTransverse kick of the di-EM system to account for ISR effectsIntegration over parton distribution functions (CTEQ4L and other modern p.d.f.)K-factor correction to the cross sections Both SM and gravity effects

MC Simulation of the ED signatures

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M(EM-EM)cos(θ

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σσσσ8 MS = 1 TeVn=4


Summary of the Backgrounds

SM backgrounds in the MC:Drell-Yanγγ (gg → γγ is negligible ! not included)

Other SM backgrounds are mostly at low masses and are completely negligible:

W+j/γ < 0.4%WW < 0.1%top < 0.1%Z → ττ < 0.1%Z+γ < 0.01%Other < 0.01%

Instrumental background from jj/jγ → γγdue to jets fragmenting in a leading π0

Determined w/ the data from a single EM trigger with 40 GeV threshold by applying probability for a jet to fake an EM object of (0.18 ±±±± 0.04)%, independent of ET and ηInstrumental background (mostly jj) is ~7%

Conservatively ignore small backgrounds

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γγ

gg →γγ

SM background dominates byThe qq → γγ at high masses


MC Description of the Data and Systematics

Kinematic distributions are well describedwith the sum of the SM and instrumental backgroundsThe following systematic errors on the differential cross sections have been identified and taken in the account:

Additional 10% conservative systematic error is assigned to address a small normalization discrepancy for released ETcuts (see cross-checks)

Agreement between the MC and the data

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16%Overall

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UncertaintySource


Fitting Procedure: Extracting Gravity Effects

Bin the data in a M×cosθ* grid (up to 40×10 bins; M∈ [0,2 TeV], cosθ*∈ [0,1])Parameterize cross section in each bin as a bilinear form in η: σ = σSM+ησ4+η2σ8

Use Bayesian fit with flat prior (in η) to extract the best value of η and 95% C.L. intervals:

Also cross-check with a simple maximum likelihood method

( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) 950

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.|;|maxˆ

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NPdNP

BNPSS

dSbb

dbA

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LdtSn

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Sb

ijijji ij

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DØ Results - IComparison of the data with the SM predictions

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Dielectrons and diphotons

ET(EM) > 45 GeV|η| < 1.1 or 1.5 < |η| < 2.5

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Fake background

Note zero-events bins at high masses!

Instrumentalbackground

Comparison of the data with the SM predictions

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Data agree well with the SM


DØ Results - IIData are in a good agreementwith the SM predictions

Comparison of the data and the SM predictions

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pBMass cut


High-Mass Candidate Events

Parameters of the two high-mass candidate events:

18.8 GeV00.84520 GeV-1.590.99132 GeV134 GeVee15 GeV-34 cm1167484582

11.7 GeV00.86575 GeV-1.911.9881 GeV81 GeVγγ15 GeV3.6 cm2750690578

PT-kickNjetcosθ*Mη2η1ET2ET

1TypeMETZvtxEventRun

Event display of the event with thehighest mass observed in Run I

M(γγ) = 574 GeVcosθ* = 0.86


Expected SignalData do not support extra dimensions hypothesisNo excess of events is seen at high masses and low scattering angles, where the signal is expected to exhibit itselfIn the absence of evidence for extra dimensions we proceed with setting limits on their size

Comparison of the data and the SM predictions

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MS=1 TeV, n=4

SM Data

Bayesian Likelihood

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DØ Limits on Large Extra Dimensions

For n > 2 MS limits can be obtained directly from η limitsFor n = 2, use average s for gravity contribution (4444s5555 = 0.36 TeV2, see hep-ph/9909218)As n = 2 case has been ruled out by cosmological constraints, and is within the reach of the current gravity experiments, such an approximation is good enoughFinally, translate limits in Hewettand GRW frameworks for easy comparison with other experiments:

MS(Hewett) > 1.1 TeVΛT(GRW) > 1.2 TeV

This limits are comparable with the final limits expected from LEP2They are complementary to those from LEP2, as they probe much higher range of s

Limits on Large Spatial Extra Dimensions

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n = 6, MS > 1.0 TeVn = 7, MS > 0.95 TeV95% CL Upper

Limit on F/M S4

F = 2/(n-2), n > 2

F = 2log( ), n = 2

(after Han et al.

PRD 59 (1999) 1050060)

MS

0.6 TeV

DØ Preliminary^

^^


Cross-Checks: Lower ET(EM)-Cut

We attempted to lower the ET(EM) cut to 25 GeV for cross-checksThere is no unprescaled background trigger available with such a low threshold, so the background statistics at high masses is very lowThere is a slight discrepancyobserved in the upper tail of the Z-peak, around 120 GeV, which would have resulted in 10% normalization uncertainty, had the ET(EM) cut been lower than it was set in the analysisIn order to account for this slight discrepancy, a conservative, 10% systematic error has been assignedto account for this effectWe are working on addressing this slight discrepancy which has to do with vertex mis-reconstruction

Agreement between the MC and the data

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ET(EM) > 25 GeV


Total background

MS=1 TeV, n=4

Slight discrepancy


Cross-Checks: pT-KickAgreement between the MC and the data

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Data Data

ET(EM) > 25 GeV ET(EM) > 25 GeV

SM expectation SM expectation


A Look in the FutureThe quest for extra dimensions is not over it has just startedWe are looking forward to CDF results on the virtual graviton effects in DY production, which will allow us to combine our limits and further restrict the large extra dimensions theoriesBoth CDF and DØ are pursuing the monojet signature a complementary way of probing extra dimensionsWe just started to be sensitive to the interesting regions in the scale MS, and Run IIA (IIB) data will allow us to double (triple) our reach (Cheung/GL, hep-ph/9909218):

Run IIA, 2 fb-1 Run IIB, 20 fb-1

l +l - + µµµµ+µµµµ- 1.3-1.9 TeV 1.7-2.7 TeVγγγγγγγγ 1.5-2.4 TeV 2.0-3.4 TeV

l +l - + µµµµ+µµµµ- + γγγγγγγγ 1.5-2.5 TeV 2.1-3.5 TeV

Run 1 Event 10 2DIMQQGRV_AHA.QPAD 2NOV99 14:50:01 7-DEC-99

PHI:

ETA:

338.

-0.28

Emax = 48.6 GeV

Et(METS)= 72.8 GeV / Phi = 157.4 Deg Sum Et = 76.2 GeV

CMP CMU

HITS EASTWEST

A monojet event as would have been seen by CDF

[courtesy M.Spiropulu]

Ultimate probe of extra dimensions will become available with the LHC and NLC(MS up to 10 TeV)


Black Hole ProductionOnce the c.m. energy exceeds the compactification scale, MS, a critical energy density is achieved and the black hole is formedNot to worry about the Earth being sucked into such a black hole; they should be constantly formed by cosmic raysThe temperature of such a black hole is: T= MPl

2/M → MS2/M × O(M/MS) ∼ MS

For MS ∼ T = 1 TeV, the black body spectrum peaks at 250 GeV, and therefore the BH technically evaporates by emitting a single energetic photon not quite a black body!Moreover, the lifetime of such a black hole is only ∼ 10-29 sThe Scwartzchild radius of such a black hole is ∼ 1/MS, i.e. its ∼ de Broglie wavelength; its not clear of one could even consider such an object as a bound state

Other possibility is evaporation in the bulk via GKK, in which case the signature is a deficit of high-s events

At a hadron collider its easy to tweak p.d.f. to account for such a deficitAt a lepton collider its hard to establish that the beams have not missed each otherin one of the well-known dimensions

Interesting possibility for a black hole is to have a color hair that holds it to our brane; if the color quantum number is conserved, the black hole could be metastable and live seconds or even days before it decays in a large number of hadrons

Look for events not in time with the accelerator clock with such a distinct signature (Dvali, GL, Matchev)


Gauge Boson ExcitationsNew developments in extra dimensions:

Randall-Sundrum two-brane model with gravity localized near the brane [PRL 83, 3370 (1999); PRL 83, 4690 (1999)]

Expect GKK resonances in, e.g., e+e- → l+l- scattering

Antoniadis/Benaklis/Quirosintermediate longitudinal extra dimensions with ∼ TeV-1 radius [PL B460, 176 (1999)]

Expect ZKK, WKK, gKK resonancesEffects also will be seen in virtual resonance exchange at lower energies

[Rizzo, hep-ph/0001247]

e+e- → µ+µ-

RS GKK

2000 3000 4000 5000 6000 70001/R (GeV)

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ts /G

eVD=2

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[ABQ, PL B460, 176 (1999)]

IBQ ZKK


Summary

DØ has completed a search for large extra dimensions via virtual graviton exchange in the diphoton and dielectron channelWe see no evidence for the signal and set restrictive limits on the energy scale of extra dimensions between 1.0 and 1.3 TeV for the number of extra dimensions between 2 and 7These limits are comparable to the final limits expected from LEP2 and are complementary in natureStay tuned for more results on Run I searches for extra dimensions from the CDF and DØ Collaborations in the next yearRun II will offer further breakthrough in the reach for the quantum gravity scale, and we are looking forward to start it in just 10 months!We will have an excellent chance to discover extra dimensions in the next Run, or to rule them out up to the mass scales ~3 TeV


Conclusion: WWW Search for Extra Dimensions

Stay tuned next generation of collider experiments has a good chance to solve the mystery of large extra dimensions!

http://www.extradimensions.com

Extra Dimensions TV Show

On 2/15/00 patent 6,025,810 was issued to David Strom for a "hyper-light-speed antenna." The concept is deceptively simple: "The present invention takes a transmission of energy, and instead of sending it through normal time and space, it pokes a small hole into another dimension, thus sending the energy through a place which allows transmission of energy to exceed the speed of light." According to the patent, this portal "allows energy from another dimension to accelerate plant growth." - from APS Whats New, 3/17/00

Carolinas Extra Dimensions

dimensions at dØsearch for large extra€¦ · fermilab w&c, 4/21/2000 greg landsberg,...

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