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Search for “Large” Spatial Extra Dimensions at the Tevatron

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Tom Ferbel

University of Rochester

Cairo - 2001

January 9-14

Search for “Large” Spatial Extra Dimensions at the TevatronThis was stolen from Greg by Tom, and edited for a 25 minute talk at Cairo

The Standard Model is recognized as a low-energy approximation to a more complete theory

This new theory supposedly takes overat some scale L, comparable to the Higgs mass, i.e., L 1 TeV

At 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) ]

Is There Life Beyond the Standard Model ?Change in Newton’s law:

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

How Does This Work?= the effective Planck Scale, MS

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!

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/R

Because 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

Kaluza-Klein GravitonsCompactified

dimension

GKK

R

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 enhanced

Low energy precision measurements are not sensitive to ADD effects

Real Gravitons

Monojets at hadron colliders

g

g

g

q

GKK

GKK

g

q

Single VB at hadron or e+e- colliders

V

GKK

V

V

GKK

GKK

GKK

V

Virtual Gravitons

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

f

f

V

GKK

GKK

f

f

V

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

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/9811291

Han, Lykken, Zhang, Phys. Rev. D59, 105006 (1999); revised version, hep-ph/9811350

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

Virtual GravitonsHewett: neither sign of the interference nor the dependence on the number of extra dimensions is specified; hence, for the interference term use ~l/MS4(Hewett), where l 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 ~1/LT4 (where LT is notation for MS)

HLZ: sign of interference and the n-dependence calculated in effective theory; with interference term ~F/MS4(HLZ), and Fcontaining explicit dependence on n:

Correspondence between formalisms:

Rule of thumb:

Hewett, GRW, and HLZ Formalismsinterference term

GKK term

SM

GKK term

Virtual Graviton Exchange at the TevatronDilepton and diphoton production via virtual graviton

- Mass 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 contribution
- Use Han/Lykken/Zhang formalism:

NLO corrections accounted

for via a constant K-factor

Dileptons:

Diphotons:

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 bycombining dielectrons and diphotons (essentially ignore tracking information), i.e., use di-EM signature!

Instrumental backgroundis not expected to be important at high mass,

hence, release strictEM-ID requirementsto maximize efficiency

Mulitjet and Direct Photon Background

SM gg 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, |h|<1.1 or 1.5<|h|<2.5, passing basic EM ID criteria:
- EMF > 0.95
- ISO < 0.10
- c2 < 100
- MET < 25 GeV
- No other kinematic restrictions in the analysis, since (M,cosq*) define the process completely
- Resulting data sample contains 1250 events
- Efficiency of the ID is determined from Z events obtained with same triggers, but lower ET(EM) threshold

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

SM backgrounds in the MC:

Drell-Yan (e-pairs)

gg(gg gg is negligible not included)

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

W+j/g < 0.4%

WW < 0.1%

top < 0.1%

Z tt < 0.1%

Z+g < 0.01%

Other < 0.01%

Instrumental background from jj/jg “gg” from jet fragmenting to leading p0

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, h)

Instrumental background (mostly jj)~7%

Ignore smaller backgrounds

Summary of Backgroundss, fb/bin

At high mass, SM background

dominated by qq gg

Total SM background

qq gg

gg gg

M(di-EM), GeV

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%)

Instrumental

background

Bin the events in a M|cosq*| grid (up to 4010 bins; M[0,2 TeV], |cosq*|[0,1])

Parameterize cross section in each bin as simple form in h: s = sSM+hs4+h2s8

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

Cross-check using maximum likelihood

n=4

MS = 1.3 TeV

MS extraction

input

expected limits:

h < 0.44 TeV-4

@ 95% C.L.

Fit MC & Data to Extract Effects of GravityLimit found: 0.46 TeV-4

Expected limit: 0.44 TeV-4

DØ Results in Di-EM Channels- High mass and small |cosq| are characteristic signatures of LED
- 2-dimensional analysis resolves LED from high-mass and large|cosq| tail from QCD diphotons
- No excess seen at high mass and large scattering angles, where LED signal is expected

For n > 2, MS limits can be obtained directly from limits on h

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 (l = -1)

LT(GRW) > 1.2 TeV

These limits are similar to most recent preliminary results from LEP2

Complementary to those from LEP2, probing different range of energies

Looking forward to limits from CDFDY analysis (MS ~ 0.9-1.0 TeV), utilizing the same technique

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

DØ Limits on Large Extra Dimensions^

hep-ex/0008065,

to appear in PRL

^

Highest-Mass Candidates

M(gg) = 574 GeV

cosq* = 0.86

Parameters of the two candidate events of highest mass:

Event with highest mass observed in Run-1

DO has searched for contributions from virtual graviton exchange in a context motivated by the possibility of there being only one scalefor particle physics, and “large” extra spatial dimensions. On the basis of the production ofmassive 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)

SummaryAngle q* 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 frame

In the presence of ISR this frame is no longer viable, and we use instead the helicity frame, defining q* 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 cosq* in the GJ and helicity frame is small (~0.05)

ISR effect is modeled in the signal MC

Since 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 ± 0.1

No FSR for true di-EM final states

q

q

Next-to-Leading Order CorrectionsEM

helicity angle

= GJ angle

q*

z

q

EM

helicity angle

EM

Boost of EM-pair

ISR

z

q*

q

EM

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