# Presentation: 607386

## Search for “Large” Spatial Extra Dimensions at the Tevatron

- Tom Ferbel
- University of Rochester
- Cairo - 2001
- January  9-14

- This was stolen from Greg by Tom, and edited for a 25 minute talk at Cairo

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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 over at some scale , comparable to the Higgs mass, i.e.,   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) ]

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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:

- = the effective Planck Scale, MS

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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!

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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

- 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 enhanced
- Low energy precision measurements are not sensitive to ADD effects

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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:

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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 ~/MS4(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 ~/T4 (where T is  notation for MS)
- HLZ: sign of interference and the n-dependence calculated in effective theory; with interference term ~F/MS4(HLZ), and F containing explicit  dependence on n:

- Correspondence between formalisms:
- Rule of thumb:

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

##             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:

- 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:

- Virtual Graviton Exchange at the Tevatron

- Dileptons:

- Diphotons:

- NLO corrections accounted
- for via a constant K-factor

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Mulitjet and Direct Photon Background

- SM  vs. instrumental backgrounds

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

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 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 > 0.95
- ISO < 0.10
- 2 < 100
- MET < 25 GeV
-  No other kinematic restrictions in the analysis, since (M,cos*) 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

| 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)% |

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Summary of  Backgrounds

- SM 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

******, fb/bin**

**M(di-EM), GeV**

- Total SM background

- qq  ****

- gg  ****

- At high mass, SM background
- dominated by qq  

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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%)**

| Source | Uncertainty |
| --- | --- |
| K-factor | 10% |
| Choice of PDF | 5% |
| Ldt | 4% |
| Efficiency | 3% |
| Overall | 12% |

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

##     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 |

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Instrumental

- background

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Monte Carlo for Signal and Background 

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Fit MC & Data to Extract Effects of Gravity 

- Bin the events in a M|cos*| grid (up to 4010 bins; M[0,2 TeV], |cos*|[0,1])
- Parameterize cross section in each bin as simple form in :  = SM+4+28
- Use Bayesian fit with flat prior (in ) to extract the best value of  and 95% C.L. intervals:
- Cross-check using maximum likelihood

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## DØ Limits on Large Extra Dimensions

- For 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 LEP2
- Complementary to those from LEP2, probing different range of energies
- Looking 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**

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## Highest-Mass Candidates

-                Parameters of the two candidate events of highest mass:

| Run | Event | Zvtx | MET | Type | ET1 | ET2 | 1 | 2 | M | cos* | Njet | 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 GeV
- cos* = 0.86

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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)

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000

## 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 frame
- In 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 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

**Boost of EM-pair **

**z**

**ISR**

**helicity angle**

- *

**q**

***EM***

***EM***

- *

**z**

**helicity angle**
**= GJ angle**

**q**

***EM***

***EM***

- Greg Landsberg, Probing Quantum Gravity in the Lab

- Fall 2000