MSc Thesis

√
A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d

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

Kuhan Wang

Supervisor: Richard Keeler
Committee Members: Michel Lefebvre, Rob McPherson
External Examiner: Michel C. Vetterli

July 1st, 2011

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√
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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√
Introduction

Introduction
We 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” MBTS
trigger
We examine the Missing Transverse Energy (MET) of
minimum bias events after selection for run, timing, jet and
track quality
The events are sorted by the number of primary vertices so as
to study the eﬀects of in-time pile-up
We compare and contrast the resolution, mean and
asymmetry of the MET with respects to global calibration
schemes and Monte Carlo results
The resolution of minimum bias events parametrized in ET
does not vary with respects to in-time pile-up, up to at least 4
vertices
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√
The Standard Model
I

The Standard Model

SM is the current theory of
particle physics
3 forces mediated by
Bosons, 3 generations of
Fermions
Fermions: Quarks and
Leptons
Quarks and Gluons carry
color charge
Quarks are color conﬁned
and must exist in a color
neutral combination

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√
Minimum Bias
I

Minimum Bias
The term “minimum bias events“ refers to selecting collision
events using an inclusive as possible trigger, with the least
amount 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 processes
characterized by low momentum transfer between the
interacting particles.
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√
The Large Hadron Collider
I


Most powerful particle
accelerator built to date
Located near Geneva,
Switzerland. Built by CERN.
26.7 km circumference
synchrotron accelerator
Peak performance - 14 TeV
√
s, 1034 cm−2 s −1
luminosity
Probe of new physics and
precision studies of the SM

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√
II

Deﬁne the luminosity,
2
Nb nb frev γr 1
L= F [ 2 ]. (2)
4π n β∗ cm s
The average number of interactions per bunch crossing is
given by,

Lσevent
Nc = . (3)
RC
For 2010, assuming an inelastic p-p cross section of 57.2 ± 6.3
this is,
5.1
Nc . (4)
NB
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√
ATLAS
I

ATLAS

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√
ATLAS
II

ATLAS

A Toroidal LHC ApparatuS, One of four major detector
experiments at the LHC
Approximately 7000 tonnes, 25 m x 44 m length by width
Inner Detector - Tracking, momentum and vertex
measurements and electron identiﬁcation
Calorimetry - energy measurements of particles except
neutrinos and muons
Muon Spectrometer - tracks charged particles that exit the
calorimeter, measures their momentum

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√
ATLAS
III

ATLAS
Minimum Bias Trigger Scintillator (MBTS) is the primary
device for observing minimum bias events in ATLAS
Dedicated machine for observing minimum bias events
Mounted on the A and C sides of the detector

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√
Pile-up
I

In-time Pile-up is the phenomena of multiple proton-proton
collisions 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 one
bunch crossing is given by,

e −λ λn
P(n) = A . (5)
n!
The number spectrum, λ, is a function of the luminosity, L, bunch
separation, Tc and cross section for the interaction, σpp ,

λ = LTc σpp. (6)

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√
Missing Transverse Energy
I

N N
Miss Miss
EX = − Ei sin θi cos φi , EY = − Ei sin θi sin φi . (7)
i=1 i=1

Miss Miss Miss
ET = (EX )2 + (EY )2 , (8)

Miss
EY
φX ,Y = arctan( Miss
). (9)
EX

The missing transverse energy per event is the negative of the vector sum of the
energy deposited into the calorimeter in an event
Closely related to this concept is the scalar sum given by,

N
ET = Ei sin θi . (10)
i
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√
II

Miss
EX ,Y are constructed as,
Miss Miss,calo Miss,cryo Miss,muon
EX ,Y = EX ,Y + EX ,Y + EX ,Y . (11)
Miss,calo
In the case of reﬁned calibrations, EX ,Y is constructed such
that,
Miss,calo Miss,e Miss,γ Miss,τ Miss,jets Miss,µ Miss,CellOut
EX ,Y = EX ,Y +EX ,Y +EX ,Y +EX ,Y +EX ,Y +EX ,Y .
(12)
Constructing the MET as seen above will give the measurement at
electromagnetic 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 for
hadronic energy signals in the calorimeter
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√
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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√
Analysis
Selection I

Analysis
Selection histograms, electromagnetic energy scale

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√
Analysis
Selection II

Analysis
Selection histograms, GCW energy scale

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√
Analysis
Selection III

Analysis
Selection histograms, LCW energy scale

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√
Analysis
Pile-up I

Analysis

Distribution of vertices per event, Data (left) and Monte Carlo (right).

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√
Analysis
Pile-up II

Analysis
Miss Miss Miss
ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). Electromagnetic energy scale.

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√
Analysis
Pile-up III

Analysis
Miss Miss Miss
ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). GCW energy scale.

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√
Analysis
Pile-up IV

Analysis
Miss Miss Miss
ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). LCW energy scale.

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√
Analysis
Pile-up V

Analysis
Average ET as a function of the number of primary vertices per event.

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√
Analysis
Resolution I

Analysis
Let’s quantify the resolution
Miss and E Miss in
Parametrize EX ET
Y

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√
Analysis
Resolution II

Analysis
Slice the result in vertical segments of ET .
Each slice is Gaussian distributed in EX Miss and E Miss .
Y
Miss
If you did this for ET , the slices would be Rayleigh distributed.

Add the histograms of EX Miss versus ET and EY Miss versus ET together
- This assumes that σX = σY .
Fit each slice of this new 2D histogram to a gaussian function,
2 2
f (x) = √ 1 2 e −(x−µ) /2σ
2πσ
Plot the values of the ﬁtted σ as a function of the ET , do this for 1 vertex
events, 2 vertex events...so forth
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√
Analysis
Resolution III

Analysis

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√
Analysis
Resolution IV

Analysis
Miss
Since σX = σY , σT for ET goes as,
Miss
∂ET ∂E Miss
(∆ET )2 = (
Miss
Miss
∆EX )2 + ( T ∆EY )2
Miss
Miss
Miss
(13)
∂EX ∂EY

(EX ∆EX )2 + (EY ∆EY )2
Miss Miss Miss Miss
= Miss
(14)
(ET )2
Miss Miss
∆EX = ∆EY

(EX )2 + (EY )2
Miss Miss
=( Miss )2
)(∆EX ,Y )2 = (∆EX ,Y )2
Miss Miss
(15)
(ET

Miss Miss
Thus, if σX = σY , the resolution of EX ,Y is the resolution of ET .
Miss Miss
Assumption: EX and EY are uncorrelated.

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√
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 resolution
parametrized 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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√
Analysis
Resolution VIII

Analysis
Fit Parameters with respect to the resolution for data (left) and Monte Carlo (right).

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√
Conclusions
I

Conclusions

We analyzed the MET in minimum bias events in the context
of in-time pile-up
Our primary was goal was to study the MET resolution with
respects to in-time pile-up
We ﬁnd that the MET resolution parametrized in ET does
not qualitatively change with regards to the number of
primary vertices
These results are reproduced in Monte Carlo and at e/m,
GCW and LCW calibrated energy scales.

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√
Backup
I

Backup

In addition to the resolution we examined the bias of the
MET parametrized in ET and the asymmetry in the φX ,Y
Miss
distribution of ET
We ﬁnd a bias in the mean, µX and µY , that is approximately
linear with respects to ET
We examine this eﬀect by looking at the asymmetry in the
φX ,Y distribution, sorted with respects to the number of
primary vertices per event
We can approximate the asymmetry using a simple model of
detector misalignment as shown.

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√
Backup
Resolution IX

Analysis

Is σX = σY ?
Easy to check in terms of ET

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√
Backup
Resolution X

Analysis

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√
Backup
Resolution XI

Analysis

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√
Backup
Mean I

Analysis
How is the mean, µX ,Y , eﬀected by pile-up?

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√
Backup
Mean II

Analysis

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√
Backup
Mean III

Analysis

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√
Backup
Asymmetry I

Analysis

A good way to understand the mean is to examine the
E Miss
quantity φX ,Y = arctan( EY ), this is the azimuthal direction
Miss
X
Miss
of the ET

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√
Backup
Asymmetry II

Analysis

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√
Backup
Asymmetry III

Analysis

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√
Backup
Asymmetry IV

Analysis
We quantify this as a
misalignment of the nominal
and real origins of the detector
If we source the MET from the
incorrect O’ the azimuthal
angle φ will be related to φ
by,

k + r sin φ
φX ,Y = arctan( ).
h + r cos φ
(17)
dN
This gives dφ ,

dN h cos φ + k sin φ + 1
∼ 2
dφ h + k 2 + 1 + 2(h cos φ + k sin φ )
(18)
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√
Backup
Asymmetry V

Analysis
We can see how well this simple model works by making a ﬁt.
1 Vertex events at electromagnetic scale from data

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