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Tom Ferbel University of Rochester Cairo - 2001 January 9-14. Search for “Large” Spatial Extra Dimensions at the Tevatron. This was stolen from Greg by Tom, and edited for a 25 minute talk at Cairo.

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search for large spatial extra dimensions at the tevatron
Tom Ferbel

University of Rochester

Cairo - 2001

January 9-14

Search for “Large” Spatial Extra Dimensions at the Tevatron

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 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:


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 ?
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:

How Does This Work?

= the effective Planck Scale, MS

effectively makes gravity strong
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!

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/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 Gravitons





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

signatures for large extra dimensions at the tevatron
Real Gravitons

Monojets at hadron colliders









Single VB at hadron or e+e- colliders









Virtual Gravitons

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









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

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/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 Gravitons
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 ~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 Formalisms
virtual graviton exchange at the tevatron
interference term

GKK term


GKK term

Virtual Graviton Exchange at the Tevatron

Dilepton 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



search at d
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
Mulitjet and Direct Photon Background

SM gg vs. instrumental backgrounds

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

data selection and efficiency
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
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 backgrounds
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 Backgrounds

s, 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
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%)



fit mc data to extract effects of gravity
Bin the events in a M|cosq*| grid (up to 4010 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


MS = 1.3 TeV

MS extraction


expected limits:

h < 0.44 TeV-4

@ 95% C.L.

Fit MC & Data to Extract Effects of Gravity
d results in di em channels
Limit 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
d limits on large extra dimensions
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



to appear in PRL


highest mass candidates
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)

next to leading order corrections
Angle 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



Next-to-Leading Order Corrections


helicity angle

= GJ angle





helicity angle


Boost of EM-pair