Search for “Large” Spatial Extra Dimensions at the Tevatron

Tom FerbelUniversity of

Rochester

Cairo - 2001January 9-14

This was stolen from Greg by Tom, and

edited for a 25 minute talk at Cairo

Is There Life Beyond the Standard Model ?The Standard Model is recognized as a low-energy approximation to a more complete theoryThis new theory supposedly takes over at some scale , comparable to the Higgs mass, i.e., 1 TeVAt one time, there were two serious candidates for such a theory:

SUSY Strong Dynamics

But more recently, it has been suggested that there may be no other scale, and that the SM model is fine up to some effective “Planck” scale of ~ 1 TeV

[ Arkani-Hamed, Dimopoulos, Dvali (1998) ]

How Does This Work?

Change in Newton’s law:

Ruled out for huge extra dimensions, but not for sufficiently small n compactified extra dimensions of size R:

1

2123

212

11

nnn

PlPl r

mm

Mr

mm

MrV

= the effective Planck Scale, MS

Rr

rR

mm

MrV

nnnPl

for

1 2123

Effectively Makes Gravity Strong

G’N = 1/MS2 GF MS 1 TeV

More precisely, from Gauss’s Law:

There are very few tests of Newton’s Law at distances smaller than 1 mm

Consequently, large spatial extra dimensions compactified at sub-millimeter scales cannot be excluded!

nPl

nS RMM 22

4 106

3 3

2 7.0

1 108

2

1

12

12

2

n,m

n,nm

n,mm

n,m

M

M

MR

n/

S

Pl

S

Kaluza-Klein Gravitons

Compactified dimensions greatly increase the strength of gravitational interactions through Kaluza-Klein “winding” modes or GKK gravitons

From the point of view of a (3+1) space-time, the Kaluza-Klein graviton modes are massive, with the mass excitation spaced 1/RBecause the mass per excitation mode is 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

Compactified dimension

R

GKK

Flat

dimension

Each Kaluza-Klein graviton mode couples with gravitational strength For the large number of modes, accessible at high energies, gravitational coupling is therefore greatly enhancedLow energy precision measurements are not sensitive to ADD effects

Signatures for Large Extra Dimensions at the Tevatron

Kaluza-Klein gravitons couple to the energy-momentum tensor, and therefore contribute to most SM processes

Since gravitons can propagate in the bulk, from our perspective in (3+1) space-time, energy and momentum will appear not to be conserved in GKK emission

Since the spin-2 graviton, in general, has a momentum component in the bulk, its spin from the point of view of our brane can appear to be 0, 1, or 2

Depending on whether the GKK leaves our brane or remains virtual, collider

signatures can include single photons/Zs/jets with missing ET,, or pair produced objects

Real Gravitons Monojets at hadron colliders

GKK

gq

q GKK

gg

g

Single VB at hadron or e+e- colliders

GKK

GKK

GKK

GKK

V

VV V

Virtual Gravitons Fermion or VB pairs at hadron or e+e- colliders

V

V

GKKGKK

f

ff

f

Virtual Gravitons For the case of pair production, amplitude for gravity contribution interferes with the SM (e.g., l+l- production):

Production cross section has three terms: SM, interference, and direct gravity The sum in KK states is divergent in the effective theory, so calculation of cross sections, requires explicit cutoff Expected value of the cutoff is MS (the scale at which effective theory breaks down, and string theory must be used)

Three different conventions used for writing an 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

All are completely equivalent, and only the definitions of MS differ:

M,cosfM

nbM,cosf

M

nadMcosd

d

dMcosd

d

*

S

*

S

*SM

*

2814

22

Hewett, GRW, and HLZ Formalisms

Hewett: neither sign of the interference nor the dependence on the number of extra dimensions is specified; hence, for the interference term use ~/MS

4(Hewett), where is of order 1, and ±1

GRW: sign of the interference is fixed, but the dependence on number of extra dimensions not

specified; therefore, interference term is ~/T

4 (where T is notation for MS)

HLZ: sign of interference and the n-dependence calculated in effective theory; with interference term ~F/MS

4(HLZ), and F containing explicit dependence on n:

Correspondence between formalisms:

Rule of thumb:

GRWHewett TSM

41

2

2 2

22 , log

2

n,n

nsM S

F

HLZHewett 44 2 SS MM

F

HLZGRW 44

1

ST M

F

51

nSS MM HLZHewett

4

nST M HLZGRW

Dilepton and diphoton production via virtual gravitonMass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/9904234; Cheung, Phys. Rev. D61, 015005 (2000), Phys. Lett. B460, 383 (1999),…]Improvement [Cheung, Landsberg, PRD 62, 076003 (2000)]: simultaneous analysis of mass and angular distributions (J=2 graviton different angular distributions from SM )There are three terms: SM, interference, and direct graviton contributionUse Han/Lykken/Zhang formalism:

Virtual Graviton Exchange at the Tevatron

*

4cos, z

M S

HLZ

F

Dileptons: Diphotons:

2 2

22 , log

2

n,n

nsM S

F

822

42

2121

8222

4222

44

2

2

2121

2

512

61

12

21

2

96

1

MM

zzKxfxfdxdx

MzMQez

Qe

M

zKxfxfdxdx

dzdM

d

qg

qq

qq

q

GKK termSM

interference term

GKK term

NLO corrections accounted for via a constant K-factor

Search at DØ

First search for large extra dimensions at Tevatron

Based on Cheung/Landsberg, with following modifications:

DØ detector does not have a central magnetic field, hence cannot measure electric charge of electrons use |cos*|

Dimuon mass resolution at high mass is poor do not use dimuons

Dielectron and diphoton efficiencies are only moderate (~50%) due to tracking inefficiency (for electrons) and conversions or overlap of photons with random tracks maximize DØ discovery 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 mass,

hence, release strict EM-ID requirements to maximize efficiency

Mulitjet and Direct Photon Background

SM vs. instrumental backgrounds

[Landsberg & Matchev, PRD 62, 035004 (2000)]

Data Selection and Efficiency

Use entire Run-1st luminosity, low-threshold, di-EM triggers: Ldt = 127 6 pb-1

Offline criteria: Exactly 2 EM clusters, ET >5 GeV, ||<1.1 or 1.5<||<2.5, passing basic EM ID criteria:

EMF > 0.95ISO < 0.102 < 100

MET < 25 GeV No other kinematic restrictions in the analysis, since (M,cos*) define the process completely

Resulting data sample contains 1250 eventsEfficiency of the ID is determined from Z events obtained with same triggers, but lower ET(EM) threshold

Criterion # of events

Starting sample 87,542

Quality criteria 82,947

2 EM 82.927

=2 EM 82,425

ET > 25 GeV 36,409

Acceptance 30,585

EM ID 10,711

ET > 45 GeV 1,250

Criterion Signal Efficiency

EM ID (87 2)%

MET < 25 GeV (98 1)%

Event quality (99.8 0.1)%

Overall, per event

(79 2)%

Monte Carlo for Signal and Background

Based on Cheung/Landsberg LO parton level generator that produces weighted events

Augmented with fast parametrized DØ detector simulation that models:

DØ detector acceptance and resolutions

Primary vertex smearing and resolution

Effects of additional vertices from multiple interactions in the event

Transverse kick of the di-EM system to account for ISR effects

Integration over parton distribution functions (CTEQ4LO and other PDFs)

K-factor correction to cross sections

Both SM and gravity effects

Summary of BackgroundsSM backgrounds in the MC:

Drell-Yan (e-pairs)(gg is negligible not included)

Other SM backgrounds are mostly at low mass, and negligible:

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

Instrumental background from jj/j “” from jet fragmenting to leading 0

Determined from data with single-EM triggers (40 GeV threshold) & applying probability of (0.18 0.04)%, for a jet to mimic photon - independent of (ET,Instrumental background (mostly jj)~7%

Ignore smaller backgrounds

, f

b/b

in

M(di-EM), GeV

Total SM

backgroundqq

gg

At high mass, SM background

dominated by qq

MC Description of Data and Systematics

Kinematic distributions are well described by the sum of SM and instrumental backgrounds

Following systematic uncertainties on differential cross sections were taken into account:

Instrumental background (uncertain to 25%)

Source Uncertainty

K-factor 10%

Choice of PDF 5%

Ldt 4%

Efficiency 3%

Overall 12%

Observe good agreement in

Mass cutoff N B P

> 100 GeV 687 682 0.43

> 150 GeV 134 138 0.63

> 200 GeV 53 52.2 0.47

> 250 GeV 18 23.5 0.90

> 300 GeV 10 11.4 0.70

> 350 GeV 5 5.8 0.69

> 400 GeV 3 3.0 0.58

> 450 GeV 2 1.5 0.44

> 500 GeV 2 0.67 0.15

> 550 GeV 1 0.23 0.21

> 600 GeV 0 <0.1 1.00

Instrumentalbackground

Monte Carlo for Signal and Background

SM 4

8 MS = 1 TeVn=4

Fit MC & Data to Extract Effects of Gravity Bin the events in a M|cos*| grid (up to 4010 bins; M[0,2 TeV], |cos*|[0,1])Parameterize cross section in each bin as simple form in : = SM+4+28

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

Cross-check using maximum likelihood

950

22

1

95

0

2

20

2

20

.|;|maxˆ

,|expexp|

,!

,|,

NPdNP

BNPSS

dSbb

dbA

NP

LdtSn

BSenBSBNP

Sb

ijijji ij

ijijijijij

MS extraction

input

n=4MS = 1.3 TeV

expected limits: < 0.44 TeV-4

@ 95% C.L.

DØ Results in Di-EM Channels

High mass and small |cos| are characteristic signatures of LED

2-dimensional analysis resolves LED from high-mass and large |cos| tail from QCD diphotons

No excess seen at high mass and large scattering angles, where LED signal is expected

Limit found: 0.46 TeV-4

Expected limit: 0.44 TeV-4

DØ Limits on Large Extra DimensionsFor n > 2, MS limits can be obtained directly from limits on For n = 2, use average s for gravity contribution ( s = 0.36 TeV2)

Translate limits in the Hewett and GRW frameworks for ease of comparison with other experiments:

MS(Hewett) > 1.1 TeV and 1.0 TeV ()T(GRW) > 1.2 TeV

These limits are similar to most recent preliminary results from LEP2Complementary to those from LEP2, probing different range of energiesLooking forward to limits from CDF DY analysis (MS ~ 0.9-1.0 TeV), utilizing the same technique

Sensitivity is limited by statistics; reach in terms of MS will double in Run-2a (2 fb-1) and triple in Run-2b (20 fb-1)

^

^hep-ex/0008065,to appear in PRL

Highest-Mass Candidates

Parameters of the two candidate events of highest mass:

Run Event

Zvtx MET Type

ET1 ET

2 1 2 M cos*

Nje

t

PT-kick

90578

27506

3.6 cm

15 GeV

81 GeV 81 GeV 1.98

-1.91

575 GeV

0.86 0 11.7 GeV

84582

11674

-34 cm

15 GeV

ee 134 GeV

132 GeV

0.99

-1.59

520 GeV

0.84 0 18.8 GeV

Event with highest mass observed in Run-1

M() = 574 GeVcos* = 0.86

Summary

DO has searched for contributions from virtual graviton exchange in a context motivated by the possibility of there being only one scale for particle physics, and “large” extra spatial dimensions. On the basis of the production of massive e-pairs and di-photons, such a scale, must be higher than ~ 1 TeV

More studies are being pursued at both DO and CDF, and can be expected to start converging in winter 2001. These will be both on virtual-graviton exchange as well as real graviton (mono-jet) production.

Run-2 will (eventually) be sensitive to scales of 3-4 TeV

The LHC will be able to access effective “Planck” scales of > 10 TeV

And now back to musing on Flatland (such stuff as dreams are made on)

Next-to-Leading Order Corrections

Angle * in the parton-level cross section is defined as the angle between the incoming parton from p and the l+, i.e. in the Gottfried-Jackson frameIn the presence of ISR this frame is no longer viable, and we use instead the helicity frame, defining * as angle between the direction of the di-EM system (boost) and the direction of EM object in that frame.ISR-induced “smearing”, i.e. the difference between cos* in the GJ and helicity frame is small (~0.05)ISR effect is 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 ± 0.1No FSR for true di-EM final states

Boost of EM-pair

z

ISR

helicity angle

*

q

q

EM

EM

*

z

helicity angle= GJ angle

q q

EM

EM