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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
A Study of Missing Transverse Energy inMinimum Bias Events with In-time Pile-up at
The Large Hadron Collider using√s=7 TeV data
Kuhan Wang
Supervisor: Richard KeelerCommittee Members: Michel Lefebvre, Rob McPherson
External Examiner: Michel C. Vetterli
July 1st, 2011
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Outline
Outline
1 Introduction
2 The Standard Model
3 Minimum Bias
4 The Large Hadron Collider
5 ATLAS
6 Pile-up
7 Missing Transverse Energy
8 Data Selection and Monte Carlo
9 Analysis
10 Conclusions
11 Backup
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Introduction
IntroductionWe examined approximately
∫L dt = 3668 nb−1 of data
taken at the LHC at√s =7 TeV during 2010
Minimum bias events are selected using a “single arm” MBTStriggerWe examine the Missing Transverse Energy (MET) ofminimum bias events after selection for run, timing, jet andtrack qualityThe events are sorted by the number of primary vertices so asto study the effects of in-time pile-upWe compare and contrast the resolution, mean andasymmetry of the MET with respects to global calibrationschemes and Monte Carlo resultsThe resolution of minimum bias events parametrized in
∑ET
does not vary with respects to in-time pile-up, up to at least 4vertices
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
The Standard Model
I
The Standard Model
SM is the current theory ofparticle physics
3 forces mediated byBosons, 3 generations ofFermions
Fermions: Quarks andLeptons
Quarks and Gluons carrycolor charge
Quarks are color confinedand must exist in a colorneutral combination
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Minimum Bias
I
Minimum Bias
The term “minimum bias events“ refers to selecting collisionevents using an inclusive as possible trigger, with the leastamount of selection, kinematic or topological
Define the minimum bias cross section σMB ,
σMB = σSD + σDD + σND + σCD . (1)
Minimum bias events are typically soft hadronic processescharacterized by low momentum transfer between theinteracting particles.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
The Large Hadron Collider
I
The Large Hadron Collider
Most powerful particleaccelerator built to date
Located near Geneva,Switzerland. Built by CERN.
26.7 km circumferencesynchrotron accelerator
Peak performance - 14 TeV√s, 1034 cm−2s−1
luminosity
Probe of new physics andprecision studies of the SM
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
The Large Hadron Collider
II
The Large Hadron Collider
Define the luminosity,
L =N2bnbfrevγr4πεnβ∗
F [1
cm2s]. (2)
The average number of interactions per bunch crossing isgiven by,
Nc =LσeventRC
. (3)
For 2010, assuming an inelastic p-p cross section of 57.2± 6.3this is,
Nc '5.1
NB. (4)
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
ATLAS
I
ATLAS
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
ATLAS
II
ATLAS
A Toroidal LHC ApparatuS, One of four major detectorexperiments at the LHC
Approximately 7000 tonnes, 25 m x 44 m length by width
Inner Detector - Tracking, momentum and vertexmeasurements and electron identification
Calorimetry - energy measurements of particles exceptneutrinos and muons
Muon Spectrometer - tracks charged particles that exit thecalorimeter, measures their momentum
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
ATLAS
III
ATLASMinimum Bias Trigger Scintillator (MBTS) is the primarydevice for observing minimum bias events in ATLASDedicated machine for observing minimum bias eventsMounted on the A and C sides of the detector
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Pile-up
I
In-time Pile-up is the phenomena of multiple proton-protoncollisions occuring in one bunch crossing
This is estimated by the number of primary vertices in the event.
The probability of in-time pile-up is governed by Poisson statistics
The probability P(n) for n independent events occuring in onebunch crossing is given by,
P(n) = Ae−λλn
n!. (5)
The number spectrum, λ, is a function of the luminosity, L, bunchseparation, Tc and cross section for the interaction, σpp,
λ = LTcσpp. (6)
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Missing Transverse Energy
I
Missing Transverse Energy
EMissX = −
N∑i=1
Ei sin θi cosφi , EMissY = −
N∑i=1
Ei sin θi sinφi . (7)
EMissT =
√(EMiss
X )2 + (EMissY )2, (8)
φX ,Y = arctan(EMissY
EMissX
). (9)
The missing transverse energy per event is the negative of the vector sum of theenergy deposited into the calorimeter in an event
Closely related to this concept is the scalar sum given by,
∑ET =
N∑i
Ei sin θi . (10)
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Missing Transverse Energy
II
Missing Transverse Energy
EMissX ,Y are constructed as,
EMissX ,Y = EMiss,calo
X ,Y + EMiss,cryoX ,Y + EMiss,muon
X ,Y . (11)
In the case of refined calibrations, EMiss,caloX ,Y is constructed such
that,
EMiss,caloX ,Y = EMiss,e
X ,Y +EMiss,γX ,Y +EMiss,τ
X ,Y +EMiss,jetsX ,Y +EMiss,µ
X ,Y +EMiss,CellOutX ,Y .
(12)
Constructing the MET as seen above will give the measurement atelectromagnetic energy scale
There are two global calibration schemes
Global Cell energy-density Weighting (GCW)
Local Cluster Weighting (LCW)
These correct for dead and malfunctioning cells and correct forhadronic energy signals in the calorimeter
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Data Selection and Monte Carlo
I
Data Selection and Monte Carlo
Our data selection criteria is as follows -
Trigger: L1 MBTS 1
GRL
Timing- LAr Calorimeters- MBTS
Bad jets- HEC Spike- e/m Coherent Noise- Beam Background
Ugly Jets
Track Quality- ≥ 1 Primary vertex, > 5 Tracks, Pt > 150 MeV
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Selection I
AnalysisSelection histograms, electromagnetic energy scale
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Selection II
AnalysisSelection histograms, GCW energy scale
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Selection III
AnalysisSelection histograms, LCW energy scale
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Pile-up I
Analysis
Distribution of vertices per event, Data (left) and Monte Carlo (right).
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Pile-up II
AnalysisEMissT ,
∑ET , EMiss
X and EMissY . Data (crosses) and Monte Carlo (bars). Electromagnetic energy scale.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Pile-up III
AnalysisEMissT ,
∑ET , EMiss
X and EMissY . Data (crosses) and Monte Carlo (bars). GCW energy scale.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Pile-up IV
AnalysisEMissT ,
∑ET , EMiss
X and EMissY . Data (crosses) and Monte Carlo (bars). LCW energy scale.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Pile-up V
AnalysisAverage
∑ET as a function of the number of primary vertices per event.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution I
Analysis
Let’s quantify the resolution
Parametrize EMissX and EMiss
Y in∑
ET
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution II
AnalysisSlice the result in vertical segments of
∑ET .
Each slice is Gaussian distributed in EMissX and EMiss
Y .
If you did this for EMissT , the slices would be Rayleigh distributed.
Add the histograms of EMissX versus
∑ET and EMiss
Y versus∑
ET together- This assumes that σX = σY .Fit each slice of this new 2D histogram to a gaussian function,
f (x) = 1√2πσ2
e−(x−µ)2/2σ2
Plot the values of the fitted σ as a function of the∑
ET , do this for 1 vertexevents, 2 vertex events...so forth
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution III
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution IV
Analysis
Since σX = σY , σT for EMissT goes as,
(∆EMissT )2 = (
∂EMissT
∂EMissX
∆EMissX )2 + (
∂EMissT
∂EMissY
∆EMissY )2 (13)
=(EMiss
X ∆EMissX )2 + (EMiss
Y ∆EMissY )2
(EMissT )2
(14)
∆EMissX = ∆EMiss
Y
= ((EMiss
X )2 + (EMissY )2
(EMissT )2
)(∆EMissX ,Y )2 = (∆EMiss
X ,Y )2 (15)
Thus, if σX = σY , the resolution of EMissX ,Y is the resolution of EMiss
T .
Assumption: EMissX and EMiss
Y are uncorrelated.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution V
Analysis
We quantify the resolution with respect to the∑
ET as,
σX ,Y =√A∑
ET ⊕√B∑
ET , (16)
We are interested in how the behaviour of the resolutionparametrized in
∑ET changes as a function of the number of
primary vertices in events, i.e. in-time pile-up
Qualitatively, from the plots shown above, they don’t really change.
NOTE TO SELF THIS IS: σX ,Y =√
A∑
ET + B(∑
ET )2
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Analysis
Resolution VIII
AnalysisFit Parameters with respect to the resolution for data (left) and Monte Carlo (right).
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Conclusions
I
Conclusions
We analyzed the MET in minimum bias events in the contextof in-time pile-up
Our primary was goal was to study the MET resolution withrespects to in-time pile-up
We find that the MET resolution parametrized in∑
ET doesnot qualitatively change with regards to the number ofprimary vertices
These results are reproduced in Monte Carlo and at e/m,GCW and LCW calibrated energy scales.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
I
Backup
In addition to the resolution we examined the bias of theMET parametrized in
∑ET and the asymmetry in the φX ,Y
distribution of EMissT
We find a bias in the mean, µX and µY , that is approximatelylinear with respects to
∑ET
We examine this effect by looking at the asymmetry in theφX ,Y distribution, sorted with respects to the number ofprimary vertices per event
We can approximate the asymmetry using a simple model ofdetector misalignment as shown.
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Resolution IX
Analysis
Is σX = σY ?
Easy to check in terms of∑
ET
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Resolution X
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Resolution XI
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Mean I
Analysis
How is the mean, µX ,Y , effected by pile-up?
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Mean II
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Mean III
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Asymmetry I
Analysis
A good way to understand the mean is to examine the
quantity φX ,Y = arctan(EMissY
EMissX
), this is the azimuthal direction
of the EMissT
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Asymmetry II
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Asymmetry III
Analysis
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Asymmetry IV
Analysis
We quantify this as amisalignment of the nominaland real origins of the detector
If we source the MET from theincorrect O’ the azimuthalangle φ′ will be related to φ′
by,
φX ,Y = arctan(k + r sinφ′
h + r cosφ′).
(17)
This gives dNdφ′ ,
dN
dφ′∼ h′ cosφ′ + k ′ sinφ′ + 1
h′2 + k ′2 + 1 + 2(h′ cosφ′ + k ′ sinφ′)(18)
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A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data
Backup
Asymmetry V
AnalysisWe can see how well this simple model works by making a fit.1 Vertex events at electromagnetic scale from data
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