Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.
-
Upload
pauline-paul -
Category
Documents
-
view
222 -
download
0
Transcript of Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.
![Page 1: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/1.jpg)
Alan Barr University of Oxford
DMUH, July 2011
LHC (ATLAS)Dark Matter SEARCHES:
UNCERTAINTIES
![Page 2: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/2.jpg)
WARNING• Theme is certainties
and uncertainties• Not a standard “ATLAS Searches” talk• Some topical analysis highlights• Concentrate on how uncertainties
determined
?
![Page 3: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/3.jpg)
Dark Matter Highlights100 GeV 1 TeV
Jets [b-tag(s)]Leptons [electron(s), muon(s)]Missing transverse momentum PT
miss
![Page 4: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/4.jpg)
![Page 5: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/5.jpg)
ATLAS-CONF-2011-086
Example conference note
![Page 6: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/6.jpg)
Example conference note
• 7 Page note– 1 Page introduction– 1 Page definitions
–2.5 pages on uncertainties– 1.5 page results/interpretation
• 10 public plots of control measurements• Dozens of others made internally
ATLAS-CONF-2011-086
>200 page internal document describes cross-checksand uncertainty determination for this one analysis (not public)
![Page 7: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/7.jpg)
Fiducial cuts
ATLAS-CONF-2011-086
165 pb-1
![Page 8: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/8.jpg)
Counts, expectations and uncertainties
ATLAS-CONF-2011-086
165 pb-1
![Page 9: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/9.jpg)
Expected Observed
![Page 10: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/10.jpg)
What we do NOT do…
Do not boldly extrapolate taking “uncertainty” fromfit
![Page 11: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/11.jpg)
Uncertainties?
Standard Model backgrounds
Instrumental backgrounds
Expected Signal?
![Page 12: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/12.jpg)
Momentum imbalance…
Mismeasurement? Cosmics? Noise? Beam halo?
Neutrinos?WIMPs?
PATHOLOGIES
PHYSICS
![Page 13: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/13.jpg)
JETS + MISSING MOMENTUM
From collisions
Jets
PTmiss
Jets
![Page 14: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/14.jpg)
JETS
From collisions
Jets:Had. CalorimeterE.M. CalorimeterTracks from vertexIn-time
b,c quark jets can decayto neutrinos
![Page 15: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/15.jpg)
JETS + MISSING MOMENTUM
MeasurementsJets: cut
Reduce:Had. CalorimeterE.M. CalorimeterTracks from vertex
Measure remainderat small
![Page 16: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/16.jpg)
JETS + MISSING MOMENTUM
From cosmics
Reduce by: (a) requiring tracks with jets(b) look for muon hits
Measure remainder: (a) no beam(b) timing
![Page 17: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/17.jpg)
JETS + MISSING MOMENTUM
From beam halo
Reduce by requiring tracks with jetsMeasure remainder with single beam / timing
![Page 18: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/18.jpg)
JETS + MISSING MOMENTUM
Calorimeter noise
Reduce by requiring tracks with jets
Measure remainder (a) no beam(b) timing
![Page 19: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/19.jpg)
Neutrinos
Z ( ) + jets
W ( l) + jets
(+ jets)
B jets
![Page 20: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/20.jpg)
Calibration, confirmations, cross-checks
Multiple MEASUREMENTS of background processes(together with theoretical predictions)
108 W bosons
2.5 107 Z bosons
> 105 top quarks
![Page 21: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/21.jpg)
W + Jets
MEASUREMENTStest MC simulations
Huge numbers of Ws
Differential in many parameters
ATLAS-CONF-2011-060
![Page 22: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/22.jpg)
Monte Carlo uncertainties State of the art generators
LO NLO NNLO Decreasing uncertainties from higher order corrections
Very non-Gaussian uncertainties Somewhat arbitrary “uncertainty” untrusted
Full GEANT detector simulations Remarkably good description of detector response
Multiple cross checks
![Page 23: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/23.jpg)
Do we trust the Monte Carlo?
Reduce use of Monte Carlo wherever possible
Background determined from MEASUREMENTS where possible uncertainties under experimental control
![Page 24: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/24.jpg)
Final results depend largely on measurements from control regions
Jets
Z + jetsJets
![Page 25: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/25.jpg)
Final results depend largely on measurements from control regions
Jets
Zμμ + jetsJets
![Page 26: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/26.jpg)
Final results depend largely on measurements from control regions
Jets
PhotonJets
+ jets
![Page 27: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/27.jpg)
A distribution we care about:
Full SimulationMonte Carlo
(Alpgen)
Leading Order
Multi-leg
![Page 28: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/28.jpg)
+ Jets( Z+jets)
Multijets
W + Jets 𝑡 𝑡
What we DO do
![Page 29: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/29.jpg)
Other uncertainties include Luminosity:
MEASURED in Van-der-Meer scans, … Proton Structure:
MEASURED at HERA ep collider Cross-checked/refined with LHC data
JET Energy Scale (detector response) MEASURED in beam tests Cross-checked/refined with LHC data
Dependence on these effects (and on MC) greatly reduced by measuring background rates in LHC data
![Page 30: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/30.jpg)
H8 calorimeter beam test 1999
JET ENERGY SCALE?
![Page 31: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/31.jpg)
Putting it together: Likelihood
Poisson for signal region
Poisson for control regions(fns of nuisance parameterssignal strength, …)
Nuisance parameters largely uncorrelated
Shifts due to nuisance parameter
![Page 32: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/32.jpg)
Sources of systematics considered
Jet energy scale Jet energy resolution Lepton efficiency Lepton energy scale
B-tag efficiency
Pile-up/multiple pp interactions
Out-of-jet energy
Monte Carlo stats MC higher order
corrections Loss of electronics
PDFs Signal cross section
higher order corrections
![Page 33: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/33.jpg)
CAVEAT
I have emphasised that multiple measurements give good confidence in size of uncertainties
RMS of measurements/discrepancies often used to define 1-sigma [~fine]
Anyone who believes in Gaussian uncertainties in such contexts is naive
One should be correspondingly wary about literal interpretations of multi-sigma effects
![Page 34: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/34.jpg)
Add additional uncertainties in predicted signal (PDF, higher orders)
Results from EPS-2011on Saturday
Full talkSimplified model
![Page 35: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/35.jpg)
![Page 36: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/36.jpg)
I CAN’T RESIST SHOWING…
![Page 37: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/37.jpg)
Con
sist
ency
with
BG
-onl
y hy
poth
esis
“Intriguing” Higgs results
![Page 38: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/38.jpg)
Getting the results?
ATLAS public resultsEPS 2011, 21-27 July; linkSupersymmetry searches summary
![Page 39: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/39.jpg)
Most recent results being presented
![Page 40: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/40.jpg)
EXTRA SLIDESLHC PHYSICS
![Page 41: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/41.jpg)
2011 Plans…
![Page 42: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/42.jpg)
Detector & Upgrade
Grid
Operations
Computing
Software
Hardware
![Page 43: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/43.jpg)
Further search papers
Others Monojets e-mu resonances Dilepton resonances
Leptoquarks CHAMPS Dimuons (contact)
W' l Z' l l
Supersymmetry: Squarks or gluinos
Lepton + jet + invis
Dilepton + invis
Same sign leptons + invis
Z + invis
b-jet(s) + invis
R-hadrons
![Page 44: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/44.jpg)
![Page 45: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/45.jpg)
Supersymmetry
Partner particles Spin differ by ½ Stabilise mH
Dark Matter candidates
“Missing” momentum
Big reach at LHC
![Page 46: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/46.jpg)
Supersymmetry searches
“Missing” momentum Scalar sum of momentum
ATLAS-CONF-2011-086
![Page 47: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/47.jpg)
Wider interpretation...
http://arxiv.org/abs/1103.0969
Allanach, Khoo, Lester, Williams
Cassel, Ghilencea, Kraml, Lessa, Rosshttp://arxiv.org/abs/1101.4664
Points sampled from fits to global data Global CMSSM fits
Regions with low fine tuning
ATLAS 0/1 leptonATLAS-CONF-2011-086
CMS αT June’11
Jan’11
h
H~𝐵
~𝐻
![Page 48: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/48.jpg)
Example Simplified Model
Squarks:
Jet
Neutralino
OtherParticles
2 Jets
![Page 49: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/49.jpg)
Example Simplified Model
Gluinos:
Jets
Neutralino
4 Jets
![Page 50: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/50.jpg)
Example Simplified Model
Squarks:
Gluinos:
Jet
Jet
Neutralino
4 Jets
![Page 51: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/51.jpg)
Example Simplified Model
Squarks:
Gluinos:
Jets
Jet
Neutralino
6 Jets
![Page 52: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/52.jpg)
arXiv:1107.2092New J. Phys. 13 (2011) 053044
![Page 53: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/53.jpg)
A year is a long time at the LHC
July 2010 July 2011 x
Bunches / beam 25 1380 55
Protons / bunch 2 x 1010 1.2 x 1011 6
Lumi / day 60 nb-1 50 pb-1 800
Integrated 200 nb-1 1.4 fb-1 7000
Commissioned bunch trains50 ns bunch-crossing operation
![Page 54: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/54.jpg)
1 fb-1 target
Technical Stop
![Page 55: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/55.jpg)
“Seeing” WIMPs at the LHC
Time
standard
two exotics
Production part
Time
standard
heavyexotic lighter
exotic
Decay partTime
Complete event
= exotic= standard
Jets [b-tag(s)]InvisiblesPerhaps leptons or photons
![Page 56: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/56.jpg)
Pileup The pileup in 2011 is on average
<μ>=6 interactions per crossing Significantly higher than 2010
And than originally anticipated in early LHC running
Tails up to 14 interactions per crossing Due to some bunches with much higher
currents Causes challenge for physics
analyses and software Detailed simulation models both the <μ>
and the bunch train structure Reweighted according to data <μ> distribution
Software performance significantly improved to accommodate Tier0 resources (reco time 11-13s/event)
Physics performance reasonably unaffected
Jet energy scale uncertainty temporarily increased for low pT jets
![Page 57: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/57.jpg)
![Page 58: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/58.jpg)
![Page 59: Alan Barr University of Oxford DMUH, July 2011 LHC (ATLAS) Dark Matter S EARCHES : U NCERTAINTIES.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d005503460f949d2bff/html5/thumbnails/59.jpg)
arXiv:1107.2092