how not to use the monte carlo
DESCRIPTION
How not to use the Monte Carlo. Stan Bentvelsen Nordic LHC workshop. Remarks 1. Proton-proton collisions are extremely complex Detectors like Atlas and CMS are extremely complex Do not thrust too much your event generator Do not thrust too much your detector simulation - PowerPoint PPT PresentationTRANSCRIPT
How not to use the Monte Carlo
Stan BentvelsenNordic LHC workshop
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Remarks 1
Proton-proton collisions are extremely complexDetectors like Atlas and CMS are extremely complex
Do not thrust too much your event generatorDo not thrust too much your detector simulation
without explicit and full checks with the ‘data’ itself
‘Data’ can be any of the following and more: Other experiments (Tevatron) Internal (sub-) detector consistency Test-beam Cosmic rays Proton-proton collisions
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Remarks 2
For reliable results the game to play is: reduce the dependency on MC as much as possible
(best to eliminate any dependence)
‘Shake down’ of detector (simulation) in many ways Redundancy between detectors Straight tracks, energy clusters, etc, etc…
Use Physics: available ‘candlelight’ signals Mass of the J/ψ, W±, Z0, top-quark Presence of b-jets
Use constraints: e.g. energy-momentum Difficult in pp collisions: Partonic cm not known Balance in PT
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Remarks 3
This does not mean to sit back and wait for data to come!
Make clever use of MC to construct ‘MC correction free’ observables
Realistically not always possible – find balance
This talk: just warn against using MC and simulation ‘blindly’…
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Use of MC’s
Not so straightforward to talk for one hour about “how not to use the Monte Carlo”
Instead, I like to discuss a few examples in which “awareness of Monte Carlo limitations”
plays an important role
It is also closely connected to “commissioning of the LHC detectors”
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Event generation
Preliminaries: Every generated physics process consists of two parts: Hard process: Obtained using
perturbative (LO,NLO) calculation of the probability amplitude (matrix element)
Soft(er) effects:
Initial and final state radiation (DGLAP parton showers)
Underlying event
Fragmentation and hadronisation
See talk by Leif Lonnblad
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“Pythia tells me that W+multijets is negligible background for my top study”
Make conscious choice of event generator Is process (with phase space) implemented in the Generator?
ttbar spin-correlations not implemented in Pythia or MC@NLO Don’t take ‘Herwig’ or ‘Pythia’ as the absolute truth
Clarify what aspect you want to test with the generator Sensitivity to underlying matrix element
E.g. multi-jet physics Sensitivity to soft component
E.g. exclusive resonance study Underlying events
In most practical cases both!
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Ignore new/better calculations?
A major step forward occurred with the introduction of NLO generator MC@NLO Full NLO QCD calculations
Practicalities: Deal with negative weights: ±w
Many generators available for multi-parton final states AlpGen, VecBos, AcerMC, Sherpa
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ttbar system: MC@NLO, Herwig, Pythia
PT(tt system) Herwig & MC@NLO agree at low PT,
At large PT MC@NLO ‘harder’ PYTHIA completely off
Huge difference in PT from ‘ISR’,MC@NLO coincides with NLO QCDcalculations
Example: distributions on top-anti-top characteristic – PT of the whole system
PT of t-tbar system is balanced by ISR & FSR
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Next step: the simulation
Detector response Parameterization, smeared
Simple detector geometry (e.g. cells in grid eta-phi) Smear 4 vector of final state particles
Photons: resolution by EM calorimeter Electrons, muons: resolutions by EM calorimeter and Inner Detector Hadrons: collected in cells – cell smearing – jet finding
E.g. b-tagging of jets implemented by overall tagging efficiency and truth information.
Detailed simulation of material interactions Geant4 (C++) packages (Geant3 is currently phased out) Detailed description of material interactions of the detector
Detailed detector geometry description Definition of ‘sensitive materials’: energy lost accumulated Creation and tracking of daughter particles: shower development
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Digitization / reconstruction
Digitization Transform accumulated energy
deposits into detector output Energy deposit in Si wafer
readout channel Physics modeling quite involved
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Simulation/data analysis flow
Energy depositions
HitsG4 Sim
PileUp
Digitization Raw Data
Objects
Simulation response
Services:
-Atlas geometry
-Alignment dBase
Reconstruction
ATLAS Bytestream
Atlas detector response
Physics analysis
objects
Postscript
(publications)
Reconstruction and analysis
Event generation
Event generation (Pythia…)
Fast simulation / parametrization
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How not to use the simulation
Fast / full simulation have both their merits and are useful
Judge for each problem what to use CPU power available Time Status
Probably not efficient to: Study cracks in the calorimeter with parameterized simulation Asses signal of various models of black hole evaporation with full simulation
(event generation should be enough!)
If time and CPU power permits – full simulation seems always ‘better’ But life is not that straightforward ‘back of envelope’ calculations often useful to test new ideas
Rule of thumb:
Detector simulation takes 1s for 1 GeV dumped energy on modern PC.
I.e. ~1 hour to generate 1 ‘heavy’ event
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How to check the Monte Carlo itself?
Tune the Monte Carlo response with test-beam data Absolutely essential! Few examples in last part of this talk
Internal consistency checks Does the detector respond symmetrically in z? Uniform in φ? Any other symmetry axis?
Inspection of the geometry – material distribution All detectors-components installed that should be installed? Compare the total ‘weight’ of a sub-detector with the weight in the
simulation
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Monte Carlo validation
Validate the full Monte Carlo simulation itself. Is geometry correct?
R (cm)
Z (cm)
Location of secondaries from truth.
TRT C-wheels missing
2nd layer pixel missing
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A few case studies
Using data to set the energy scales Calorimeter scale: using Z0
B-jet scale: using Z0
Et-miss
Using data to check/study data B-jet calibration W-mass determination Top physics
Underlying event B-taggin efficiencies Non W QCD background
Testbeam We have already data!
What do we learn from that?
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Event rates in ATLAS or CMS at L = 1033 cm-2 s-1
Already in first year, large statistics expected from: -- known SM processes understand detector and physics at s = 14 TeV -- several New Physics scenarios
Which physics in first year?
Process N/s N/yearTotal collected before start LHC
W e 15 108 104 LEP / 107 FNAL
Z ee 1.5 107 107 LEP
tt 1 107 104 Tevatron
bb 106 1012-13 109 Belle/BaBar ?
H (130) 0.02 105 ?
Low lumi
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Energy scale calibration
Make use of physics signals to understand the detector Abundance of Z and W particles being produced Top quark Various combinations of these with associated particles
Z-boson: Properties extensively determined at LEP Mass and width known up-to approx 2 MeV Mass and couplings described by Standard Model
W-boson: Current precision on mass approx 42 MeV
Ultimate goal at LHC to bring down to ~15 MeV
Top-quark Current mass at 178±4 GeV
Ultimate goal at LHC aprox 1 GeV
PDG Mass (GeV) Width (GeV)
Z 91.1876±0.0021 2.4952±0.0023
W 80.425±0.038 2.124±0.041
Top 178±4
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Z0e+e- calibration
Use the Z0 mass to calibrate the EM calorimeterCan we get non-uniformity and absolute energy scale from data? Divide the calorimeter in regions i Introduce bias for each region by The Z0 invariant mass
Can be written as:
By giving all αi a suitable variance, a likelihood fit can be constructed Determine βij with lots of Z0
Untangle the αi
)1( itruei
newi EE
)cos1(2 truej
truei
trueij EEM
21
21 ijtrue
ijjitrue
ijnewij MMM
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Ze+e- calibration
Method works well From parametrized MC study a
good correlation is observed between the fitted and injected values for α
Test method on full simulation events Expect non-uniformity due to
material distribution
Difference αinj and αfit
Integrated over regions in φ as function of η
Energy-loss due to material
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Hadronic shower components
A hadronic shower consists of EM energy (e.g. ),
O(50%) Visible non-EM energy (e.g.
dE/dx from , , etc), O(25%) Invisible energy (e.g. breakup
of nuclei and nuclear excitation) O(25%)
Escaped energy (e.g. Ν) Each fraction is E
dependent and subject to large fluctuations
Calibration has to take into account both visible and invisible energy fractions: delicate process
Energy scale of jets can have miscalibration as large as 5-10%
Invisible energy is the main source of the non-compensating nature of hadron calorimeters
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Jet energy calibration
Can we utilize the EM scale to say something on hadronic scale?
Use lepton balancing in PT to calibrate the jet energy Again – use the MC to check if the method works in an unbiased way. But method should be independent of MC as possible
Jets energy calibration not straightforward Both hadronic and electromagnetic energy content. No unambiguous assignment of energy-flow to a jet.
Which particles belong to the jet and which don’t?
%3%50)(
%9)(
EE
EE
e
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Calibration of b-jets using Z or
B-jet response different from light quark jet
fragmentation – invisible component …
Rely on relatively rare process Process :
g + b b + Z0 b jet + +-
Constraint : pT(b) pT(Z0)
First estimation of calibration constant : = pT(2)/ pT(jet)
Use precise muon tracking to study the scale of b-jets
M(Z)=91.2 GeV
(b-tagged) Jet
MC study:
g + q q + Z0 signal
q + q g + Z0 with g qq background
Jet reconstruction with Cone algorithm
R = 0.7
pTseed = 5 GeV; pT threshold = 15 GeV
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Event selection: Z0+jet
Statistics not great for Z0+jet – but enough to do the analysis
-1 bjet + +- reproducing invariant mass of Z0
-no photons, no electrons
Event generated : 30 000 000; events selected : 20 000pT(2) in GeV Nb of events pT(2) in GeV
40-50 7589 44.5
50-60 4494 54.5
60-75 3552 66.6
75-120 3554 91.7
120-200 931 145.0
> 200 119 257.0
Expected number of events in 3 years of low luminosity runs
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Imbalance in PT
Due to Initial State Radiations :
the pT balance is not fully verified
the reconstructed b jet can come from ISR
PT(2) [GeV/c]
pT(b) / pT(2)
40-50 0.961 0.003
50-60 0.969 0.003
60-75 0.973 0.003
75-120 0.971 0.003
120-200 0.979 0.006
>200 0.98 0.03
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Use the MC to evaluate the balance between pT(b) and pT() Introduce dependence on ISR of MC Check the MC by evaluate distribution in φ
K= (pT(jet) + pT().cos(φ/2) is sensitive to ISR
φ is the angle between pT(jet) and pT()
RMS (K) can be used to evaluate ISR effects from real data side
How to deal with imbalance?
φ
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Potential of + jet
The statistics is much better in this case
Analysis: selection, optimized for jet rejection
• Opposite hemisphere : most energetic jet + loose back-to-back requirement ±0.3 in
azimuth
Pt balance mean
Quark 2.6 %
Jet particle level 19 %
Jet em scale -5.8 %
Jet hadronic calibration 21%
Example Cone jet R=0.7
Imbalance between photon and quarks, particles, EM jets and Had jets
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+jet or Z0+jet in-situ processes
Which useful information can be extracted from these processes ?
Pro’s and Z0 are “electromagnetic objects”, calibrated at a well-known
scale the selection of the jet can be independent of the jet finding
algorithm, jet fragmentation, etc... by selecting simply the highest ET jet in the opposite hemisphere to the or Z0
comparative jet algorithm studies can be done: difference in calibration between different jet algorithms, relative efficiencies, etc.
+jet with pT>20 GeV: ~ 10k events in 1 minute but identification efficiency & trigger!
can be used to calibrate calorimeter region with dead material, uniformity scans, monitoring, etc.
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Con’s or Z0 is not an unbiased estimator of the back-to-back parton
because of ISR and FSR Difficulty for absolute energy scale : this applies particularly in the low
pT range up to ~ 40 GeV the background to the or Z0 may bring an additional bias
The background will be more severe for ’s that for Z0
the pT range covered with good statistics may be limited The effect of the trigger has also to be considered (standard menu or
downscaled)
+jet or Z0+jet in-situ processes
W-mass determination
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W-mass determination
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Measurement by comparing MC
Relevant quantities Hadronic recoil U PT of the muon
I.e. for correct transverse mass MT the PT of the recoil U is needed
Straightforward MC method: Construct MC ‘template’ for MT by
taking into account: Initial State Radiation Angular distributions Recoil model Detector resolution
Fit template to data to extract MW
Not the best method! Heavily rely on details of event
generation, Monte Carlo simulation.
Can one be a bit clever and reduce dependency on MC?
W
ν
Hadronic recoil
up anti-downUPEE T
missTT
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MW by comparison to Z data
Use data from process Z Factor 10 lower cross section, but
with abundant Z production no problem
Substitute one muon by a neutrino Z-decays have almost identical
topology
Calculate MT(Z) from remaining muon and recoil Use the precise knowledge of MZ
Transform MT(Z) distribution to MT(W) distribution and extract MW/MZ. Take difference of production
mechanism into account
Reduce MC dependency MC only needed to predict effect
of topology difference (small effect)
Determination of a ratio and MZ to determine MW
Z
Hadronic recoil
up anti-down
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Analysis
To compare W and Z samples: Use technique to create MT
templates for arbitrary mass and width:
Use both muons to reconstruct Z Boosts muons into Z rest frame Set Z mass to arbitrary new value
MX, and width ΓX. Consider one muon to be a
neutrino Calculate outgoing 4 vectors Boost back into LAB frame Calculate MT
X from recoil and remaining muon
Compare many MTX templates
with the observed, measured MT
W distribution, to extract MW as MX.
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Analysis and worries..
Now MW can be determined from fit to templates MT(W) Very small uncertainties With 106 events uncertainty
~10 MeV (stat)
Test method on fully simulated events
Use MC to assess Final State Radiation effects Neutrino does not radiate Muon does radiate
Completely different use of the MC!
Top physics
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Top studies
Top physics at LHC Top one of ‘easiest’ bread and butter
Cross section 830±100 pb
Used as calibration tool What variations in predictions of t-tbar
– which generator to use? Underlying event parameterization Background estimation from MC
Tuning b-tagging at startup Jet energy scale
Try to be as independent from MC as possible.
Semi-leptonic top channel
detector tools involved:
Lepton reconstruction
Missing ET
Jets + calibration
B-tagging
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Lepton + jet: reconstruct top
Hadronic side W from jet pair with closest invariant mass to MW
Require |MW-Mjj|<20 GeV
Assign a b-jet to the W to reconstruct Mtop
Kinematic fit Using remaining l+b-jet, the leptonic part is
reconstructed |mlb -<mjjb>| < 35 GeV Kinematic fit to the tt hypothesis,
using MW constraints
j1
j2
b-jet
tW-mass Selection efficiency 5-10%
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High Pt sample
The high pT selected sample deserves independent analysis: Hemisphere separation (bckgnd reduction, much less combinatorial) Higher probability for jet overlapping
Use all clusters in a large cone R=[0.8-1.2] around the reconstructed top- direction Less prone to QCD, FSR,
calibration UE can be subtracted
j1
j2
b-jet
t
Statistics seems OK but what about syst?
R
Mtop Mtop
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Underlying event evolution
It is not only minimum bias event!
The underlying event is everything except the two outgoing hard scattered jets.
In a hard scattering process, the underlying event has a hard component (initial + final-state radiation and particles from the outgoing hard scattered partons) and a soft component (beam-beam remnants).
ljet
CDF analysis:• charged particles: pt>0.5 GeV and |η|<1
• cone jet finder:
7.022 R
UE is defined as the Transverse Region
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LHC predictions: UE
Tra
nsv
erse
< N
chg >
Pt (leading jet in GeV) Tevatron
x 4
x 5
LHC
x 3
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Top-quark production UE
Charged particle density in pseudorapidity: Tevatron and LHC predictions.
Widly different predictions!
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Jimmy UE: Cells & Jets
Herwig vs Jimmy LO t-tbar
At jet-level effectreduced
10 GeV
Cell multiplicity
Cluster multiplicity
Jet multiplicity
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Reconstruct the top
Top peak for various reconstruction methods Difference in mass can be as large
as 5 GeV
Really need data to check data on UE Study effect better with data itself!!
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Background events
Top physics background Mistags or fake tags Non-W (QCD) W+jets, Wbbar, Wccbar Wc WW,WZ,ZZ Z tt Single top
~ 150 pb-1 W+4jet background Not completely trivial to generate
Can we observe the top without b-tagging?
Largest background is W+4 jet.
This background cannot be simulated by Pythia or Herwig shower process. Dedicated generator needed: e.g. AlpGen. Large uncertainties in rate
Ultimately, get this rate from data itself. For example, measure Z+4 jets rate in data, and determine ratio (Z+4 jets)/(W+4 jets) from MC
W+4 extra light jets
Jet: Pt>10, ||<2.5, R>0.4
No lepton cuts
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Non btag: top sample
Signal plus background at initial phase of LHC
Most important background for top: W+4 jets Leptonic decay of W, with 4 extra ‘light’ jets
With extreme simple selection and reconstruction the top-peak should be visible at LHC
L = 150 pb-1
(2/3 days low lumi)
Selection: Isolated lepton with PT>20 GeV
Exactly 4 jets (R=0.4) with PT>40 GeV
Reconstruction: Select 3 jets with maximal
resulting PT
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Extraction of top signal
Fit to signal and background Gaussian signal 4th order polynomal Chebechev background
Extract
cross section
and Mtop?
150 pb-1
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Select the 2 jets with highest resulting PT W peak visible in signal No peak in background Better ideas well possible!
E.g. utilizing 2 body decay in top rest frame.
Select 2 jets with invariant mass closest to Mw (80.4 GeV) Large peak in background Enormous bias Not useable!
150 pb-1
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Fit to W mass
Fit signal and background also possible for W-mass Not easy to converge fit
150 pb-1 mean σ(stat)
in peak 3.0% 5%
Mtop 167.0 0.8
Mw 77.8 0.7
With W sample we can check the jet energy scales
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Jet Energy scale / MC dependence
Variation of the jet energy scale to infer systematics Bjet scale: 0.92 – 0.96 – 1.00 – 1.04
– 1.08 Light scale:0.94 – 0.98 – 1.00 – 1.02 – 1.04
(1) (2) (3) (4) (5)
1) Analysis with jet energyscaled
2) All with MC@NLO, Herwigand Pythia;
3) Redo analysis with doubled W+4jet background (stat indep)
Top mass
155
160
165
170
175
180
0 5 10 15 20 25
Scale variations
To
p m
ass
Raw Top Mass
Scaled Top Mass
Determine Mtop and σ(top)
‘Raw’, i.e. no correction for jet scale
‘Corrected’, i.e. apply percentage difference of W-peak to the reconstructed top
Dependence on top mass reduced by scaling with W:
Rms Raw: 6.2 GeV
Rms Scaled: 1.2 GeV
Top mass rescaled using W constraint
‘Raw’ Top mass
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Some results… (still no b-tag)
To summarize: We can ‘easily’ observe top mass peak
Sideband subtraction: limited sensitivity to background
From this sample we see the W-mass peak Rescale the jet energies
Select pure top sample Use to obtain b-tagging efficiencies
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Lower luminosity?
Go down to 30 pb-1 Both W and T peaks already
observable First check of jet energy scale
30 pb-1 mean σ(stat)
in peak 0.8% 17%
Mtop 170.0 3.2
Mw 78.3 1.030 pb-1
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Use exclusive b-decays with high mass products (J/) Higher correlation with Mtop Clean reconstruction (background free) BR(ttqqb+J/) 5 10-5 ~ 30% 103 ev./100 fb-1
(need high lumi)
Top mass from J/
Different systematics (almost no sensitivity to FSR)
Uncertainty on the b-quark fragmentation function becomes the dominant error
M(J/+l) Mtop
M(J/+l)
MlJ/
Purely leptonic determination
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Non-W (QCD-multijet) background
Not possible to realistically generate this background Crucially depends on the detector capability to minimize
mis-identification and increase e/ separation This background has to be obtained from data itself
E.g. method developed by CDF during run-1:
Rely now on e/ separation of 10-5
Use missing ET vs lepton isolation to define 4 regions:
A. Low lepton quality and small missing ET
Mostly non-W events (i.e. QCD background)
B. High lepton quality and small missing ET
Reduction QCD background by lepton quality cuts
C. Low lepton quality and high missing ET
W enriched sample with a fraction of QCD background
D. High lepton quality and high missing ET
W enriched sample, fraction of QCD estimated by (B·C)/(A·D)
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Detector scenarios: b-tagging
Precise alignment of ID can be reached only after few months of data taking. Most precise alignment using tracks from data
Top events to evaluate b-tagging efficiencies from data Select a pure t-tbar sample with tight kinematical cuts
Count the number of events with at least 1 tagged jet Compare 0 vs 1 vs 2 b-tagged jets in top events Can expect the b-tagging efficiency different in data from MC
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Top in physics arena:
Inputs to the top analysis
Estimate of the single electron trigger efficiency Can be done by using the Z
triggered as single electron How much time is needed to arrive
to a reasonable evaluation of this efficiency?
Estimate of the initial lepton identification efficiency
Estimate of the integrated luminosity At the beginning the precision on L
should be around 10-20%. The ultimate precision should be <
5% Eventually:
B-tagging efficiency Jet scales
What top events can provide
Top candidates enriched samples A “pure” one, obtained with quite
tight selection criteria A “loose” one: a more “background
enriched” sample, to be used as control sample for background calculations etc…
Estimate of a light jet energy scale correction Assume 10% for light and b-quark
jets, look at effect on Mtop and stop Assume that at the very beginning
only the EM scale is known (means: do not put any weight on the hadronic scale)
Output: provide the MW peak to rescale the light jets
Estimate of the b-tagging efficiency
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One slide on supersymmetry
Impressive result to get MSUSY
How well do we know the MC predictions?
Herwig parton shower
Matrix element MC(GeV) )(jet p E M4
1iiT
missTeff
signalEvents for 10 fb-1
background
Study of Z+jet events from data will asses the validity of the MC prediction
Testbeam
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Testbeam analysis
We have data to test/tune simulation Example: Atlas testbeam
Slice of the Atlas detector at fixed value of η~0 Useful for trigger/DAQ tests Calibration of the detector
Calorimeter calibrations ID alignment Muon r-t and alignment
Full Geant4 simulation available for the testbeam setup Check of the ‘computing model’
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Tracking
Data for tracking – to
compare to MC
9 GeV e/
B=0
Pixel+SCT+TRT
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Muons: Sagitta measurements
• Create r-z and phi track-segments, perform pattern recognition
• Segments fit on each muon station
• Combination of inner and outer,compare with middle station
• Misalignment affects mean value and width
• Multiple scattering affects width
Sagitta definition at the TB:
Sagitta
Outer
Middle
Innerstation
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Comparisons with G4 simulation
Real data/G4 sim reconstruction comparison can provide important feedback to the G4 validation effort
First tests: generate muons in the testbeam setup (only muon detectors activated for now) at beam energies measured in data• Track reconstruction• Compare fit residuals and sagitta resolution
Data=61m
G4 =57 m
MDT fit residuals
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Comparisons with G4 simulation
G4Data
Athena 8.7.0
DataG4
Athena 8.8.0
- Difference G4-Data 1/p: material problem(effect corresponding to ~ 3 cm aluminumequivalent).- Detailed check of materials associated to GeoModel volumes-problem was found in RPC
DED
RPC internal structure
After fixing the problem
Sagitta width Sagitta width
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Summary / conclusions
Use all the tools available to test the simulation prediction by using data Masses of W and Z, top Constraints
Using the simulation, the game can be prepared now
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Backup slides
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Use noise of the calorimeter
Correlations between EM and hadron calorimeter
e
Internal consistency checks useful tools to understand sub-detector
S()/N 7
Barrel middle compartment
Test-beam data
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To summarize:
We can ‘easily’ observe top mass peak
Sideband subtraction: limited sensitivity to background
From this sample we see the W-mass peak
Rescale the jet energies
Select pure top sample
Use to obtain b-tagging efficiencies
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Material Study
Attempt to recreate ATLAS inner detector material distribution at = 1.6 (DC-2)
Proposed Actual
Pixel / SCT 15% X0 / 12.5mm Al 12% X0 / 10mm Al
SCT / TRT 20% X0 / 16.7mm Al 24% X0 / 20mm Al
Some simulations with the added material have now been examined. Analysis of actual data not done yet (pending improvements in
alignment)
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Simulation
CTB-G4Sim modified to add new material. Reconstruction in e-gamma rec of 1000 single electron events @
45GeV Effect of increased brem clearly visible in E/p distribution with added
material.
Without added Material With added Material
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Different jet finder with + jet
Measured pT distribution compared to MC and to photon PT
Understanding jet-splitting, underlying event, etc