Higgs Hunt Using Expert Discriminants in the
ZH→ννbb at the TeVatron
A Senior Honors Thesis
Presented in Partial Fulfillment of the Requirements for graduation
with research distinction in Physics in the undergraduate
colleges of The Ohio State University
by
Douglas Schaefer
The Ohio State University
June 2009
Project Adviser: Professor Brian Winer, Department of Physics
Abstract
This analysis presents improved techniques applicable to searches for a low mass Higgs
boson in events with missing transverse energy and two b-quark jets at CDF. The sample
includes substantial contributions from both ZH and WH final states, as well as substantial
backgrounds originating from QCD multi-jets, tt production, heavy diboson production,
and instrumental backgrounds. Multivariate techniques have been shown to be extremely
important in increasing the experimental sensitivity in this channel. We investigate the use of
multivariate methods targeted toward rejection of specific backgrounds and how to combine
these methods to form a single overall discriminant. We present expected improvements of
14% in Higgs search sensitivity using these new techniques.
Contents
1 Introduction 1
2 Higgs Mechanism 6
3 The TeVatron and CDF 9
3.1 Collider Detector at Fermilab . . . . . . . . . . . . . . . . . . 10
3.2 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Multivariate Techniques 15
4.1 Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . 16
4.2 Boosted Decision Trees (BDT) . . . . . . . . . . . . . . . . . . 16
4.3 Support Vector Machines . . . . . . . . . . . . . . . . . . . . . 18
5 ZH/WH → MET + Jets Analysis 20
5.1 Signals ZH and WH . . . . . . . . . . . . . . . . . . . . . . . 20
i
5.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.1 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.2 Electroweak . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.3 Top . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.4 Single Top . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.5 Diboson . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 Selection Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.3.1 Kinematic Cuts . . . . . . . . . . . . . . . . . . . . . . 25
5.3.2 b Tagging . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3.3 Loosening Cuts . . . . . . . . . . . . . . . . . . . . . . 29
6 Expert Multivariate Technique 33
6.1 Track Based Variables - Track MVT . . . . . . . . . . . . . . 33
6.2 Individual Expert Discriminants . . . . . . . . . . . . . . . . . 38
6.3 Global Discriminant . . . . . . . . . . . . . . . . . . . . . . . 42
6.4 Control Region Check . . . . . . . . . . . . . . . . . . . . . . 43
7 95% Expected Confidence Level Limits on the Standard Model
Higgs Production 45
ii
List of Tables
5.1 Acceptance Efficencies of Higgs Events after all Tight Selection
Cuts in the Signal Region . . . . . . . . . . . . . . . . . . . . 30
5.2 Acceptance of Higgs Events after all Tight Selection Cuts in
the Signal Region at 1.7fb−1 . . . . . . . . . . . . . . . . . . . 30
5.3 Acceptance of Higgs Events after all Loose Selection Cuts in
the Signal Region at 1.7fb−1 . . . . . . . . . . . . . . . . . . . 31
5.4 Acceptance of Backgrounds after Tight Selection Cuts in the
Signal Region at 1.7fb−1 . . . . . . . . . . . . . . . . . . . . . 31
5.5 Acceptance of Backgrounds after Loose Selection Cuts in the
Signal Region at 1.7fb−1 . . . . . . . . . . . . . . . . . . . . . 32
7.1 95% Expected Confidence Level Limits . . . . . . . . . . . . . 47
7.2 95% Expected Confidence Level Limits . . . . . . . . . . . . . 48
iv
List of Figures
1.1 An example of the Eightfold Way, which is the meson octet. s
is the strangeness, and q is the charge of the particles. . . . . . 3
1.2 Standard Model of Particle Physics . . . . . . . . . . . . . . . 3
1.3 The Limits that have been placed on the Higgs bosons mass.
The horizontal axis is the mass of the Higgs boson, and the
vertical axis represents the ∆χ2 probability of the Higgs having
a at the given mass. The yellow portions have been ruled out
by experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 An example of a symmetric potential. . . . . . . . . . . . . . . 8
v
2.2 The Higgs Mechanism spontaneously breaks the electroweak
symmetry. V (φ) is the potential, and the x-y axes show that
the Higgs Field is a complex scalar field. The distance of the
ball from the V (φ) axis tells us the magnitude of the Higgs
field. So in the early universe when the energy was much
higher, the Higgs field did not interact with particles in such
a way as to give them mass. . . . . . . . . . . . . . . . . . . . 8
3.1 CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 A simplistic model of the path and interaction of particles in
CDF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
vi
4.1 Schematic view of a decision tree. Starting from the root node,
a sequence of binary splits discriminating variables xi is per-
formed. Each split uses the variable that at this node gives
the best separation between signal and background when be-
ing cut on. The same variable may thus be used at several
nodes, while others might not be used at all. The leaf nodes
at the bottom end of the tree are labeled S for signal and B
for background depending on the majority of events that end
up in the respective nodes. . . . . . . . . . . . . . . . . . . . . 18
5.1 Feynman Diagram for ZH Production . . . . . . . . . . . . . . 21
5.2 Feynman Diagram for WH Production . . . . . . . . . . . . . 21
5.3 One simple version of the QCD background. . . . . . . . . . . 22
5.4 Some electroweak backgrounds including Wbb and Zbb . . . . 22
5.5 Top background . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.6 The Single Top background including s-channel and t-channel.
The s-channel is more relevant after tagging because it has the
same final state as WH. . . . . . . . . . . . . . . . . . . . . . 24
5.7 Some Diboson backgrounds including ZZ and WZ . . . . . . . 24
vii
5.8 b quarks travel a distance from the interaction vertex before
they decay at a secondary vertex. . . . . . . . . . . . . . . . . 29
6.1 The Expert Multivariate Technique is a tri-leveled process of
different Multivariate techniques. Each successive layer start-
ing on the left adds more information as you go to the right. . 33
6.2 The tracks are summed up into a vector and then the magni-
tude is taken. This track based variable shows some separation
for ZH vs ZBB. . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.3 The Track MVT for ZH vs QCD. The addition of the calorime-
ter variables helped dramatically. . . . . . . . . . . . . . . . . 37
6.4 The multivariate technique with the largest integrated area
was selected to be used as the Track MVT. This is an example
from the Track MVT for ZH versus QCD. . . . . . . . . . . . 38
6.5 The individual expert discriminant for ZH vs QCD. The addi-
tion of the calorimeter variables helped dramatically. . . . . . 41
viii
6.6 The Global Discriminating neural network with equal normal-
izations for the signal and background. The signal and back-
ground shapes contain the appropriate mixing of the different
processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.7 The electroweak control region shows that the Global Expert
Discriminant is well modeled. . . . . . . . . . . . . . . . . . . 44
7.1 The expected shapes for the signal and background in the dou-
ble SecVtx category. . . . . . . . . . . . . . . . . . . . . . . . 47
ix
Chapter 1
Introduction
Since the time of the Greeks, humans have tried to understand the world around them
on a fundamental level. Aristotle theorized that the world was made of four elements: earth,
fire, water, and air. We have come a very long way from these ideas; however, we have
are still interested in the fundamental building blocks of the universe. In 1665, Robert
Hooke made a breakthrough by finding tiny components of matter, which he called cells.
Then came atoms, and slowly we began to see a pattern in the structure of atoms with the
periodic table, which is credited to Dmitri Mendeleev in 1869. The periodic table hinted at
some substructure to atoms.
In 1897, J. J. Thomson discovered the electron through his work with cathode ray tubes,
which changed the notion that atoms were the fundamental building blocks of our universe.
Ernest Rutherford, in 1909, discovered more of the substructure of atoms by shooting alpha
particles or helium nuclei at a thin sheet of gold and looking at the diffraction and reflections
of the alpha particles. Rutherford realized that atoms are mostly empty space. However,
he said that atoms seem to have hard cores, which he called the nucleus. Later came
1
the discovery of the neutron and the proton. All of these particles seemed to make sense,
even the discovery in 1932 of antimatter by Carl Anderson [2] after the prediction of their
existence by Paul Dirac in 1928. Dirac believed in his theory so much that he predicted
a new particle with his theory, and the positron or positively charged electron was born.
However, the discovery, also by Carl Anderson in 1936, of a massive version of the electron,
called a muon, made physicists very worried that all of these particles were not fitting into
some very simple overarching model. There continued to be so many discoveries of new
and interesting particles with no fundamental structure that physicists began to call them
collectively a “particle zoo.” However, this all changed with the introduction of the eightfold
way by Gell-Mann in the 1962. This gave the “particle zoo” some structure and made a
prediction of a new particle called the Ω−, which was later found in 1964. An example of the
structure that the eightfold way gave can be seen in Figure 1.1. It is interesting to look at
the eightfold way for its group theory background, and how mathematics has played a key
role in the progress of science from Einstein to Dirac.
The Standard Model of particle physics describes the interaction of all of the fundamental
particles that we know of, and it includes particles like electrons and anti-electrons called
positrons that fall into a category of particles called leptons. The components of protons
and neutrons are in the quark section with the names up and down. Another category for
matter is the bosons, which are force carriers, or particles that mediate the electromagnetic,
strong, and weak forces. Figure 1.2 shows a visual representation of all of the particles in
the Standard Model.
2
Figure 1.1: An example of the Eightfold Way, which is the meson octet. s is the strangeness,
and q is the charge of the particles.
Figure 1.2: Standard Model of Particle Physics
Now we are at a crossroads again. We have the Standard Model for particle physics,
which describes all of the fundamental particles that we know about, but the model has
the unfortunate prediction of making all of the particles massless. The aim of this thesis is
3
to improve the sensitivity to a particle called the Higgs boson, which will result from the
breaking of the electroweak symmetry of the Standard Model and give particles mass. This
is very important because we know that particles like the Z and W+/− bosons have a large
amount of mass. The Higgs boson is the simplest way of giving particles in the Standard
Model mass. There are other theories such as symmetry leaking to other dimensions [4],
technicolor [5], and top quark condensate [8], but they are beyond the scope of this paper.
The Large Electron-Positron (LEP) Collider, which was housed in the same ring as the
Large Hadron Collider (LHC) in Geneva, Switzerland, provides an experimental limit lower
bound on the Higgs boson mass of 114 GeV/c2. The LEP experiment also had approximately
a two standard deviation excess of Higgs events at a mass of 115.6 GeV/c2 [7], which is in
the mass range where my analysis is most sensitive. The TeVatron at Fermilab in Batavia,
Illinois has also ruled out the region around 160-170 GeV/c2 [3]. Finally, the theory work
that tells us that a higher mass Higgs is unlikely. This information is contained in Figure
1.3, which shows the mass regions that have been ruled out at 95% Confidence Level.
4
Figure 1.3: The Limits that have been placed on the Higgs bosons mass. The horizontal axis
is the mass of the Higgs boson, and the vertical axis represents the ∆χ2 probability of the
Higgs having a at the given mass. The yellow portions have been ruled out by experiment.
5
Chapter 2
Higgs Mechanism
The Higgs Mechanism is the easiest way to give mass to the particles in the Standard
Model, and it was discovered by Peter Higgs in 1964 as well as by Guralnik, Hagen, Kibble,
Brout, and Englert [6]. The Higgs Mechanism has the fortunate consequence of having a
particle called the Higgs Boson associated with it, which expermentalists can look for to
verify the Higgs field theory. It is interesting to note that Higgs’s paper in 1964 was rejected
by the Physics Review Letters journal because it made no measurable prediction, so Higgs
added a line at the end about creating one or more massive scalar particles [6]. Because of
that one line, the main push at the LHC is to find the “Higgs” boson.
The Higgs Mechanism is a spontaneous symmetry breaking model that allows for particles
to gain mass, and it requires a new field called the Higgs field which permeates all space
and has a non-zero vacuum expectation value. The Higgs field is a symmetric potential, like
the one in Figure 2.1. At some time in the past, the Higgs field slipped to a non-zero value,
which spontaneously broke the electroweak symmetry. The problem with any spontaneous
symmetry breaking model is that according to Goldstone’s Theorem there should be an
6
associated massless particle. However, we have not observed such a particle. Hence, the
Higgs Mechanism also needs to rule out such a Goldstone boson. Peter Higgs’s observation
was that combing a gauge theory with a spontaneously symmetry-breaking model causes the
massless boson to gain mass.
7
Figure 2.1: An example of a symmetric potential.
Figure 2.2: The Higgs Mechanism spontaneously breaks the electroweak symmetry. V (φ)
is the potential, and the x-y axes show that the Higgs Field is a complex scalar field. The
distance of the ball from the V (φ) axis tells us the magnitude of the Higgs field. So in
the early universe when the energy was much higher, the Higgs field did not interact with
particles in such a way as to give them mass.
8
Chapter 3
The TeVatron and CDF
The TeVatron particle collider near Chicago that accelerates protons and anitprotons to
a center of mass energy of 1.96 TeV . The TeVatron had two different “Runs.” Run I ran
from 1992 to 1996. We are now in Run II, which is higher in luminosity and allows for more
interactions over the same time period. Along the beam line, there are two general purpose
detectors on the TeVatron. They are called D0 and the Collider Detector at Fermilab (CDF).
Each of these detectors represent a collaboration of over 500 physicists. Using data from
Run I, CDF and D0 combined their results to discover the massive third generation quark
called the top (truth) quark in 1995 [1]. The TeVatron was then shutdown in 1996 to be
upgraded for Run II.
On March 1, 2001, the TeVatron Run II collider program began and is planned to run
through 2011. The TeVatron is running at a center of mass energy of 1.96 TeV , and the
beam luminosity is still being increased so that as much data as possible can be collected
before the final shutdown. The TeVatron should deliver around 11 fb−1 of data, and CDF
will record around 9 fb−1 that we can use in the Higgs search. The TeVatron is currently
9
the highest energy particle accelerator in the world. The TeVatron accelerates protons and
antiprotons around the 6.28 km circular tunnel. There are bunches of around 1014 protons
and antiprotons, which travel around main ring at a highly relativistic speed with bunch
crossings every 396 ns. A bunch crossing is the event when a proton cloud passes through
an antiproton cloud in the CDF or D0 detectors.
3.1 Collider Detector at Fermilab
The data I use is collected by CDF. The detector is capable of taking a large number of
measurements and identifying a wide variety of particles. We define a coordinate system in
the detector that I will use throughout the rest of this paper. The angles in the transverse
plane to the beam line are denoted by φ and vary between 0 and 2π. I will also discuss the
angle between objects when projected into the transverse plane to the beam line, and I will
denote these angles by ∆φ. Another angular measurement is the angle with respect to the
beam line, which is denoted by θ and varies between −π2
and +π2
. What is more important is
using θ to define the pseudorapidity, which is given by η = − ln[tan ( θ2)] and varies between
−∞ to ∞. Finally, we denote the total angular separation by ∆R =√
(∆φ)2 + (∆η)2.
I will now give an introduction to the different components of the detector. Starting at
the collision point and working outward, CDF has a wide variety of different components.
The protons and antiprotons are carried in the beam pipe. Immediately outside of the
beam pipe is silicon tracker, and it continues to 28 cm from the interaction point. The
newly created charged particles that leave transverse to the beam line from the interaction
point make a signature called a “hit” in some of the seven barrels of silicon. The barrels
10
are arranged in concentric circles, and the “hits” can be connected like dots to plot the
trajectory of the particles leaving the beam pipe. The silicon detector is placed in a strong
magnetic field which causes the charged particles like electron, muons, taus, and charged
hadrons to curve. This helps identify the electric charge of the particles by determining the
orientation of curvature. The silicon tracker is very sensitive and allows for the detection of
secondary interaction points. This is very important for the identification of b quarks because
they travel a small distance from the original interaction point before showering into other
particles. This is the hallmark sign of a b quark. As we will see later, the identification of b
quarks is important for the Higgs search.
The next layer of CDF is the Central Outer Tracker (COT) and goes from 28 cm to
1.3 m. The COT is filled with Argon and Ethane so that charged particles can ionize the
gas. The COT is also filled with tens of thousands of wires which are at high voltage to
collect the ions. The voltage causes the ions to cascade toward the wires and create more
electrons so that the signal is measurable. There are two types of wires called sense wires
and field wires. The sense wires detect the electrons which are ionized off of the atoms in
the gas. The field wires absorb the positive charges that are left behind from the electron
ionization.
The solenoid covers the COT and provides a strong magnetic field of 1.4 T to help identify
charged particles coming outward from the interaction point. The amount that the particles
bend also gives a measure of their momentum. The higher momentum particles have a lower
curvature while the lower momentum particles have a much higher curvature. The solenoid
is made of superconducting material and must be kept at 4.7 K to stay superconducting.
The B field from the solenoid effectively ends about 1.5 m from the beam line and is one of
11
the most important parts of the detector for the identification of charged particles.
Beyond the solenoid is the electromagnetic (EM) calorimeter, which measures the energy
of light particles like electrons and photons. The EM calorimeter is made of alternating
layers of plastic scintillator followed by 0.75 in thick sheets of lead. The change in materials
causes the high energy charged particles to emit Cerenkov radiation. Also the light electrons
emit light via Bremsstrahlung and slow down losing their energy in the scintillator. The
hadronic calorimeter surrounds the EM Calorimeter and measures the energy of particles
like protons and neutrons. The energy measurement of the neutron is the first signature
received from these neutral particles. The separation of neutral particles from charged ones
lies in the fact that charged particles should have a track that leads up to the calorimeter
tower.
The muon chambers are the most distant from the beam line, but are very important for
identifying the massive leptons. Since a lot of interesting particles like quarks can decay to
muons, it is important to identify them. The outer part of the muon chamber is essentially a
drift chamber with sense wires and is very similar to the COT, but these drift chambers are
very slow. Hence, some scintillating material was added because it can give a quick response
from the time of muon passing through the drift chamber. There is also a large amount of
steel to shield the outer layers of the muon chambers because we only want to detect muons.
Neutrinos can also pass through all of the steel; however, they are too weakly interacting to
be seen. So their existence is inferred from the conservation of momentum and energy and
not through any direct detection.
12
Figure 3.1: CDF
Figure 3.3: A simplistic portrayal of how particles behave within the CDF detector.
3.2.2 Silicon Tracking
Placed directly on the beam pipe, closest to the aftermath of a proton-antiproton
collision are the silicon detectors. The silicon detector is divided into three layered
sub-systems. Layer00 is the first sub-system, with the innermost layer positioned at
a radial distance of 1.35 cm around the beampipe. This layer must withstand the
greatest amount of radiation of any part of the detector, and is comprised of single
sided silicon wafers designed to tolerate the large bias voltages necessary. Layer 00
allows for enhanced resolution on the impact parameter associated with collisions,
and offers a layer of protection for the second silicon sub-system.
The SVX II is comprised of 5 layers of double-sided silicon. In each layer, one side
is axial, aligned to offer radial and transverse tracking information (r-φ), while the
36
Figure 3.2: A simplistic model of the path and interaction of particles in CDF.
13
3.2 Trigger System
The trigger system determines which of the 3 million collisions happening each second
should be recorded. The trigger has many different paths, but ultimately it is limited to
recording data at a rate no faster than 50 Hz. This is a factor of 50,000 smaller than the
frequency of bunch crossings. The trigger for CDF contains three levels with the first level
containing mostly hardware. The second level translates the hardware information into data
that can be read by software. The second level has around 20 µs to make its decision, so it
is pressed for time. The information is then read out for the third level of the trigger where
the event is completely reconstructed. For the purpose of this analysis, the trigger looks for
at least 2 clusters of more than 10 GeV in energy with at least one of them being central or
with |η| < 1. Also at least 35 GeV in missing transverse energy (MET) is required to keep
the event for this analysis.
14
Chapter 4
Multivariate Techniques
For my analysis, I rely on several different multivariate techniques, and I try to select the
technique that is best at extracting information to discriminate the signal from the back-
ground. Multivariate techniques use kinematic variables to identify patterns or similarities in
a class of events called the training sample, then it tests to see if this set of patterns is found
in a testing sample. The multivariate techniques try to extract as much information out of a
set of data, and this improves the efficiency of searches at the TeVatron by allowing for more
information than simple cut and count based experiments because the neural networks look
for non-linear correlations between a large number of variables. The multivariate techniques
are all trained on simulated data called Monte Carlo, which will later be verified on data.
To give a more intuitive explanation of a multivariate technique, I want to draw compare
them to the way a detective might look at clues to help identify a suspect. Similarly, multi-
variate techniques search through data looking for patterns that will allow it to distinguish
signal from background; however, multivariate techniques look at thousands of different
events to make make certain its decisions are robust. I trained a boosted decision tree, an
15
artificial neural network, and a support vector machine for ZH versus each background in-
dividually as well as WH versus each background individually.
4.1 Artificial Neural Networks
The are playing a fundamental role in the search for the Higgs boson. ANNs were used
in the 1.7 fb−1 analysis by giving them track information to separate backgrounds that were
in a large part due to poor detector resolution. Also an ANN was used as a discriminant for
the Higgs.
4.2 Boosted Decision Trees (BDT)
Boosted Decision Trees (BDT) are perhaps the simplest of the multivariate learning
techniques that I used; however, this did not stop it from being a strong performer. The
simplicity allows for the decision trees to effectively utilize more kinematic variables. The
BDTs also trains very quickly because it is entirely cut based. The BDT trains approximately
400 trees. Then the best combination of these 400 trees are used to create a single output
value called a discriminating value, which moves the signal events toward a value of 1 and
the background to a value of 0.
The BDT used is a binary decision process. Figure 4.1 shows the training for a decision
tree. The boosting refers to the training of more than one decision tree, and the weighted
combining of the trees with different signal and background normalizations reduces some
16
of the fluctuations in the training samples. AdaBoost or adaptive boost is the technique
that I used. It involves selecting the events which were most poorly identified as signal or
background and increases the percentage of these events in the next decision tree in the
forest or collection of decision trees. The increase in weighting is applied by a scalar factor
that multiples each tuple of input variables. The err function measures the amount of which
the particular event worth of information, called a tuple, is misidentified, and then the event
is scaled by the factor,
α =1− errerr
. (4.1)
Next after the training is complete, some of the overtraining must be removed in order to
get a stable output from the BDT. The cost complexity method is utilized. Cost complexity
pruning relates the number of nodes in a subtree below a node to the gain in terms of
misclassified training events by the subtree compared the the node itself with no further
splitting. The cost estimate R chosen for the misclassification of training events is given by
the misclassification rate 1−max(p, 1− p) in a node. The cost complexity, ρ, for this node
is then defined by,
ρ =R(node)−R(subtree below that node)
#nodes(subtree below that node)− 1. (4.2)
The BDT uses something called the PruneStrength, which I set to 15. It sets the maximum
for ρ, which I defined above, so the PruneStrength > ρ. The BDT starts at the highest node
on each tree and checks to see if ρ is less than the PruneStrength. If it is, then the BDT
moves done to the next layer and checks the condition that PruneStrength > ρ. This process
eliminates nodes or branches of the BDT that have very low statistics, and makes the BDT
more stable to variations in the sample that it is run over.
17
Figure 4.1: Schematic view of a decision tree. Starting from the root node, a sequence of
binary splits discriminating variables xi is performed. Each split uses the variable that at
this node gives the best separation between signal and background when being cut on. The
same variable may thus be used at several nodes, while others might not be used at all.
The leaf nodes at the bottom end of the tree are labeled S for signal and B for background
depending on the majority of events that end up in the respective nodes.
4.3 Support Vector Machines
Support Vector Machines (SVM) views the inputs as n-tuples of data. Then it removes
one variable and tries to maximize the distance between the signal and the background. So
with two variables, the SVM tries to draw a line between that optimizes the distance from
signal to background. For three variables, it looks for a plane. Then the signal should be
on one side of the plane while the background is on the other side. For n variables, the
SVM looks for an n - 1 dimensional surface called a hyperplane to separate the signal from
18
the background. The SVM takes a measurement of the distance from the hyperplane to the
event and uses this as its one dimensional output.
19
Chapter 5
ZH/WH → MET + Jets Analysis
5.1 Signals ZH and WH
This analysis deals with the Standard Model Higgs boson by looking for ZH production.
This is a Standard Model process where a virtual Z boson is produced that radiates a Higgs
boson. I look for the Z to decay to a pair of neutrinos (νν), which pass through our detector
without interacting with any component to a measurable degree, and the Higgs to decay to
a pair of b quarks (bb), which will shower into a cone shaped region that we call jets. Jets
are denoted by clusters of energy with cone 0.4, in ∆R, jets used in this analysis. Hence, as
you saw in the trigger, we look for events with large missing transverse energy (MET) and at
least two jets coming from the b quarks. ZH→ννbb production has one of the largest signal
contributions to the low mass Higgs search at the TeVatron because the branching ratio of
the Z to νν is nearly three times higher than Z→e+e− and Z→µ+µ− combined. There is
also a significant contribution to this sample, which comes from WH→lνbb. For WH to be
found in this sample, we would need to miss the lepton. There is also a separate analysis
20
which aims to use the WH events; however, they require the identification of the lepton to
be included in their analyses. Therefore, WH provides an increase in the signal sample for
my analysis on ZH production, which is important because the production of the Higgs is so
small that we must try to collect as many events as possible.
Figure 5.1: Feynman Diagram for ZH Production
Figure 5.2: Feynman Diagram for WH Production
5.2 Backgrounds
5.2.1 QCD
QCD is the largest background to MET + jets production at the TeVatron, but it is the
result of poor detector resolution because the final state of these events is not the same as
21
our signal. QCD events are produced at such a large rate that some are bound to enter the
sample.
Figure 5.3: One simple version of the QCD background.
5.2.2 Electroweak
The electroweak backgrounds include Z and W boson produced with a pair of heavy flavor
quarks. These events have the same final states as ZH and WH production, so they are very
difficult to reject. One distinction is that the quarks produced are not constrained to the
Higgs mass as in WH and ZH production. Therefore, the invariant mass is an important
variable for separating this background.
Figure 5.4: Some electroweak backgrounds including Wbb and Zbb
22
5.2.3 Top
The top quark was discovered at the TeVatron in 1995 and is a background to the Higgs
when we miss a lepton or a jet. The top quark is typically produced in pairs so we denote
the background tt, and tt is the second largest background to the MET+jets Higgs search
at the TeVatron. It is difficult to separate because it too has real MET associated with the
neutrinos.
Figure 5.5: Top background
5.2.4 Single Top
Recently discovered at the TeVatron, single top is the production of one top quark. It is
produced at a much lower rate than tt, but this analysis still accepts a large number of these
events. These events can also have some real MET. There are contributions from s-channel
and t-channel, but s-channel is the more relevant because it has the same final state at WH.
23
Figure 5.6: The Single Top background including s-channel and t-channel. The s-channel is
more relevant after tagging because it has the same final state as WH.
5.2.5 Diboson
Diboson events come from the production of a pair of vector bosons including ZZ and
WZ. These events are some of the most difficult to reject because they have the same final
states at WH and ZH production. At times, these backgrounds border on an irreducible
background. Indeed the last analysis treated them as such. However, we will see that there
is some distinguishing power that we can find in some track based variables.
Figure 5.7: Some Diboson backgrounds including ZZ and WZ
24
5.3 Selection Cuts
The various selection cuts for this analysis reduce the amount of background by a sig-
nificant amount. We hope that some cuts like the b tagging do not drastically change the
shape of the background and the signal because the training sets used in this analysis do not
require b tagging. But to take a limit of the Higgs cross-section we need to require b tagging
in order to cut the signal to background ratio to a more reasonable 1:50. While others cuts,
like the one on the angle φ between the two jets are used to define control regions for the
background. These regions are used to verify the Monte Carlo, which is simulated data used
to model the low cross-section Higgs events and their backgrounds. It is important to verify
that the Monte Carlo matches up with the data.
5.3.1 Kinematic Cuts
The MET also needs to be cleaned up to some extent, so we apply some requirements
on top of the MET35 Trigger. If more information is needed, then please consult Branon
Parks’ Thesis [9]. Here are the clean up cuts:
• At least one Z-Vertex with class > 11
• At least one track in the central tracking system with COT hits and PT > 0.5
• Require that at least 10% of the sum of all jet ET is deposited in the electromagnetic
calorimeter.
• Require that the total track PT over ET of all jets divided by the number of jets is
25
greater than 0.1.
1
Njet
Njet∑j=1
∑PT
ET> 0.1 (5.1)
• Jets that fall within 0.5 < η < 1.0 and 1.04 < η < 1.74 are often mismeasured. This
region, known as the chimney, contains a large amount of instrumentation and often
produces a second jet whose energy is measured low. Events with jets falling in this
region are vetoed.
• Tests of QCD modeling are performed in a region in which the MET is aligned with
the second jet. A large number of jets passing selection in this region are located at
|η| < 0.1. These events are removed in this region since the MET is likely due to the
instrumental effect of a large crack at η = 0. Studies of Pretag data (data prior to
tagging requirements) show that this effect is not present in the signal region.
Beyond eliminating fake MET , we also need to remove events that account for the turn on
of trigger efficiencies.
• Jets in the event are required to be separated by a cone of ∆R > 1.0 to avoid cluster
merging.
• A centrality requirement of |η| < 0.9 on at least one jet is applied due to the central
jet trigger requirement.
• A cut is placed on the missing transverse energy in the event. The MET in the event
must be recalculated after applying corrections to jets in the event. Only jets with
a raw ET > 10.0 GeV and |η| < 2.0 are corrected. The MET is then corrected by
the difference between raw and corrected ET for each jet. While the trigger threshold
26
for the uncorrected MET is set at 35 GeV , the efficiency is low for events with this
corrected MET . Therefore, a threshold of 50 GeV in corrected MET is set for an
event to be accepted.
The ZH→ννbb analysis makes some additional cuts in order to get a more pure sample
of the signal. The first set of cuts are to make sure that there are no electrons or muons in
the event coming from the primary vertex. Since a true Higgs event should have no high
energy electrons or muons coming from the interaction vertex in the final state, then we do
not want to find any in our detector. I will denote the following cuts by the name Tight
Cuts:
• Events with 2 and only 2 jets with ET > 20 GeV and |η| < 2.0(Tight) are accepted.
• If a third jet is found at high |η|(2.0 < |η| < 2.4) having a corrected ET > 20 GeV ,
the event is vetoed.
• In Higgs events, the leading jet is expected to be more energetic than that of most
backgrounds. A leading jet requirement of 45 GeV is placed on all events.
• Events with identied high-energy electrons and muons are not accepted, as these are
potential candidates for orthogonal WH searches. We implement the standard high-PT
definition of tight or loose leptons as a veto. However, we define a control region to
test trigger efficiencies and multivariate distributions as events with an identied high
PT muon.
• A cut is placed on events in which ∆φ(MET − LeadJet) < 0.8. This cut is highly
efficient for signal, and removes a portion of QCD background.
27
• The final cut placed on events is determined by the displacement between the MET
and the second jet. The region in which the MET is aligned with the second jet consists
almost entirely of multijet QCD production and is defined by ∆φ(MET−2ndJet) < 0.4.
A separate kinematic region dened by a cut of ∆φ(MET − 2ndJet) > 0.8 is used for
the final signal region and for studies of electroweak Monte Carlo backgrounds.
5.3.2 b Tagging
b tagging uses the fact that b quarks travel a distance from the interaction point, called
the primary vertex, to a secondary vertex before showering into a spray of particles called
a jet. The silicon tracking is very important for identifying the secondary vertex because
high Pt tracks can be traced back to look for intersections. Some of these intersections can
happen behind the primary vertex, and these events are called negative tags, which are used
to measure the systematic uncertainties of the b tagging. Tagging cuts out a large amount
of events without b quarks. The problem is that the efficiency for the for accepting Higgs
events after these cuts is low as can be seen in table 5.1.
28
Figure 5.8: b quarks travel a distance from the interaction vertex before they decay at a
secondary vertex.
5.3.3 Loosening Cuts
The cuts in this analysis were then loosened to allow in more signal. These cuts will be
denoted Loose Cuts, while the previous set of cuts, which were used the the 1.7fb−1 analysis,
will be denoted Tight cuts. These changes do not impact any of the control regions, so they
will not change the errors on the backgrounds in any negative manner. The changes to the
Loose Cuts are:
• ∆φ(jet2 - MET) > .4
• Et,jet1 > 35 GeV
This results in an increase in the signal acceptance of 8% for a Higgs mass of 115 GeV/c2.
However, it will also double the amount of background.
29
Table 5.1: Acceptance Efficencies of Higgs Events after all Tight Selection Cuts in the Signal
Region
Mass (GeV/c2) ZH→ννbb 2 Vtx Tags WH→lνbb 2 Vtx Tags
110 2.56% 0.69%
115 2.75% 0.72%
120 2.96% 0.76%
130 3.22% 0.80%
140 3.43% 0.91%
150 3.59% 0.91%
Table 5.2: Acceptance of Higgs Events after all Tight Selection Cuts in the Signal Region at
1.7fb−1
Mass (GeV/c2) ZH→ννbb Expected # Events WH→lνbb Expected # Events
110 0.78 0.57
115 0.68 0.49
120 0.59 0.39
130 0.38 0.25
140 0.20 0.14
150 0.08 0.05
30
Table 5.3: Acceptance of Higgs Events after all Loose Selection Cuts in the Signal Region
at 1.7fb−1
Mass (GeV/c2) ZH→ννbb Expected # Events WH→lνbb Expected # Events
115 0.73 0.53
Table 5.4: Acceptance of Backgrounds after Tight Selection Cuts in the Signal Region at
1.7fb−1
Background Expected # Events for 2 SecVtx tags Observed # Events for 2 SecVtx tags
tt 8.2 ± 1.3 8.1
single top 4.7 ± 0.8 4.6
WZ/WW 1.2 ± 0.2 1.2
ZZ 1.7 ± 0.3 1.7
W+h.f. 6.9 ± 2.9 6.5
Z+h.f/Z→ττ . 8.2 ± 3.4 7.8
Mistags 1.5 ± 0.3 1.5
QCD 15.6 ± 8.6 16.3
31
Table 5.5: Acceptance of Backgrounds after Loose Selection Cuts in the Signal Region at
1.7fb−1
Background Expected # Events for 2 SecVtx tags
tt 9.1
single top 5.3
WZ/WW 1.3
ZZ 1.8
W+h.f. 8.8
Z+h.f/Z→ττ . 9.7
Mistags 1.8
QCD 27.5
32
Chapter 6
Expert Multivariate Technique
Track MVTs
Global Discriminant for MET+bb
Individual Expert
Discriminant
Figure 6.1: The Expert Multivariate Technique is a tri-leveled process of different Multivari-
ate techniques. Each successive layer starting on the left adds more information as you go
to the right.
6.1 Track Based Variables - Track MVT
This is the first layer in the Expert Multivariate Technique as seen in Figure 6.1. The
track based variables were used previously to separate out QCD, but in figure 6.2, the
track based variables show some potential separation between ZH and Zbb. I trained a
multivariate technique with 19 track based variables, and I call the resulting network a
33
Track MVT, which looks for separation in ZH versus each of its backgrounds individually.
Then I also trained WH versus each of its backgrounds individually. The difference in
performance of these multivariate techniques justifies the separate training for WH and ZH.
The better performance of the ZH networks can be seen in figure 6.3, in which ZH seems to
be better separated than WH from each background. The separation into one signal versus
one background at a time allows the multivariate technique to optimize for each background.
The best multivariate technique is chosen by collecting the largest integral under the curve
in the signal acceptance versus background rejection plot. In cases where the techniques are
very similar, then I refer to the KS test for the technique that seems to be modeled best.
An example of the signal versus background rejection plot can be seen in figure 6.4. The
definitions of the track based variables are listed below:
• metx0Q0Pt0 -∑
Px for all deftracks with PT > 0, χ2 < 2, and #COT hits > 0 1
• mety0Q0Pt0 -∑
Py for all deftracks with PT > 0, χ2 < 2, and #COT hits > 0 1
• etQ0Pt0 -∑
PT for all deftracks with PT > 0, χ2 < 2, and #COT hits > 0 1
• mezQ0Pt0 -∑
Pz for all deftracks with PT > 0, χ2 < 2, and #COT hits > 0 1
• metxQ6Pt2 -∑
Px for all deftracks with |ztrk position − zhigh PT trk| < 5cm, PT > 2,
χ2 < 2, and #COT hits > 0 1
• metyQ6Pt2 -∑
Py for all deftracks with |ztrk position − zhigh PT trk| < 5cm, PT > 2,
χ2 < 2, and #COT hits > 0 1
• etQ6Pt2 -∑
PT for all deftracks with |ztrk position − zhigh PT trk| < 5cm, PT > 2,
χ2 < 2, and #COT hits > 0 1
34
• metxQ1Pt2 -∑
Px for all deftracks with ≥ stereo/axialSL′s, 2 < PT > 15, χ2 < 2,
and #COT hits > 0 1
• metyQ1Pt2 -∑
Py for all deftracks with ≥ stereo/axialSL′s, 2 < PT > 15, χ2 < 2,
and #COT hits > 0 1
• etQ1Pt2 -∑
PT for all deftracks with ≥ stereo/axialSL′s, 2 < PT > 15, χ2 < 2,
and #COT hits > 0 1
• metxQ2Pt2 -∑
Px for all deftracks with 2 < PT > 15, χ2 < 2, and #COT hits > 0
1
• metyQ2Pt2 -∑
Py for all deftracks with 2 < PT > 15, χ2 < 2, and #COT hits > 0
1
• etQ2Pt2 -∑
PT for all deftracks with 2 < PT > 15, χ2 < 2, and #COT hits > 0 1
• maxPx - Find the max PT track with χ2 < 2 and #COThits > 0 and use its Px1
• maxPy - Find the max PT track with χ2 < 2 and #COThits > 0 and use its Py1
• nVtx - The number of class 12 vertices
• metQ0 - Which is defined by√
(metx0Q0Pt0)2 + (mety0Q0Pt0)2
• metSigQ0 - Which is defined by etQ0Pt0√(metx0Q0Pt0)2+(mety0Q0Pt0)2
• metQ6 - Which is defined by√
(metxQ6Pt0)2 + (metyQ6Pt0)2
1
1χ2 = χ2CT(# COT hits−5) < 2
35
ZH
ZBB E
vent
s
Energy (GeV)
Figure 6.2: The tracks are summed up into a vector and then the magnitude is taken. This
track based variable shows some separation for ZH vs ZBB.
36
8
Separation of WH vs QCD Separation of ZH vs
QCD
Separation of ZH vs ttbar Separation of
WH vs ttbar
Figure 6.3: The Track MVT for ZH vs QCD. The addition of the calorimeter variables helped
dramatically.
37
Figure 6.4: The multivariate technique with the largest integrated area was selected to be
used as the Track MVT. This is an example from the Track MVT for ZH versus QCD.
6.2 Individual Expert Discriminants
While the tracking information was utilized optimally for each background, the addition
of the calorimeter information should make further improvements. This is the second layer
in the Expert Multivariate Technique. The variables, which are input into the multivariate
techniques are listed below. An Individual Expert Discriminant (IED) was trained to dis-
criminate each background from each signal individually. These IEDs will be inputs into the
final layer.
In the case of the IED, I need to prune down the number of variables, so I used perhaps
the simplest of the multivariate learning techniques to rank the variables. The Boosted
Decision Trees (BDT) allow the input of all 48 variables that I analyzed and produces a
38
rank-ordered list of these variables. All variables of at least 1% significance according to
the BDT variable ranking were selected, and this lead to an average of 19 variables in each
Individual Expert Discriminant. As for the type of multivariate technique, the BDT, SVM
- Gauss, and ANN were all trained, and then the top performing multivariate technique was
chosen by the same method as the Track MVT. The complete list of variables is listed below:
1. L5 vertex corrected MET, which I have denoted MET and is defined by
MET = METcorr = METraw −#jets∑j=1
(EL5 corrT,j − EL5 raw
T,j ) (6.1)
2. ∆R(jet1, jet2)
3. Invariant mass of the lead jet and trailing jet -
M =
√√√√(2∑j=1
Ej)2 − (
2∑j=1
Px,j)2 − (
2∑j=1
Py,j)2 − (
2∑j=1
Pz,j)2 (6.2)
4. Track based neural network trained to separate ZH from QCD and was used in the
previous analysis
5. Track MET vector dotted with the L5 vertex corrected MET vector
6.#loose jets∑
j=1
ET,j, with loose jets being defined as having PT > 12 GeV and not the lead
or trailing jet
7. ∆φ(TrackMET,L5correctedMET )
8. Fox Wolfram 1 [9]
9. Fox Wolfram 2 [9]
39
10.
MT,norm =
√√√√(2∑j=1
Ej)2 − (
2∑j=1
Px,j)2 − (
2∑j=1
Py,j)2
ET,lead jet + ET,2ndjet
(6.3)
11. ET,lead jet
12. ET,2ndjet
13. ET,lead jet + ET,2ndjet
14. ET,lead jet + ET,2ndjet +#loose jets∑
j=1
ET,j
15. ∆φ(lead jet,MET )
16. ∆φ(2ndjet,MET )
17. ∆φ(lead jet, 2ndjet)
18. Track MVT for ZH versus QCD
19. Track MVT for ZH versus Diboson
20. Track MVT for ZH versus tt
21. Track MVT for ZH versus Single top
22. Track MVT for ZH versus WBB
23. Track MVT for ZH versus ZBB
24. Track MVT for WH versus QCD
25. Track MVT for WH versus Diboson
40
26. Track MVT for WH versus tt
27. Track MVT for WH versus Single top
28. Track MVT for WH versus WBB
29. Track MVT for WH versus ZBB
30. All 19 of the track variables listed above in section 6.1
WH vs. Ttbar ZH vs. Ttbar
WH vs. QCD
ZH vs. QCD
Figure 6.5: The individual expert discriminant for ZH vs QCD. The addition of the calorime-
ter variables helped dramatically.
41
6.3 Global Discriminant
Combining the Individual Expert Discriminant and 5 important kinematic variables re-
sults in the Global Expert Discriminant. This is a Jetnet based neural network, which was
the choice I made because the last neural network was also a Jetnet ANN. This made it easy
to do some direct comparisons. The additional 5 kinematic variables are the variables that
were used in the past analysis, except I switched the track ANN for ZH versus QCD for the
loose jet energy. Here is a list of the inputs:
1. MET as defined in equation 6.1
2. ∆R(jet1, jet2)
3. Invariant Mass as defined in equation 6.2
4. Track MET • L5 vertex corrected MET
5.#loose jets∑
j=1
ET,j as defined in Section 6.2
6. All of the Individual Expert Discriminants found in Section 6.2
42
Eve
nts
Signal BKG
Global Discriminant Output
Figure 6.6: The Global Discriminating neural network with equal normalizations for the
signal and background. The signal and background shapes contain the appropriate mixing
of the different processes.
6.4 Control Region Check
The electroweak control region is important because it contains less than 1% of the signal
that is found in the signal region while containing large amounts of the backgrounds. The
Global Expert Discriminant seems to be well modeled in the control region. This tells me
that the Monte Carlo matches the data well. All of the Track MVTs and Individual Expert
Discriminants also match the data well.
43
Num
ber o
f Eve
nts
Figure 6.7: The electroweak control region shows that the Global Expert Discriminant is
well modeled.
44
Chapter 7
95% Expected Confidence Level
Limits on the Standard Model Higgs
Production
In order for us to just perform a counting experiment on the expectation of 50 background
events. To compare with the current expected statistical limits placed on Higgs boson at
115 GeV/c2, I want to ask how much data would we need to collect to obtain the same
upper limit on the Higgs production rate. The upper statistical limit on the expected Higgs
cross-section at 95% confidence is 9.2 times the expected Standard Model cross-section. So I
will calculate the number of trials or collections of 1.7 fb−1 that will be necessary to place the
same limit. If the upper limit is 9.2∗SM , then we would expect to see 9.2 Higgs events with
1.7 fb−1 of data. The null hypothesis is 48 background events. So we ask how much data
is needed to see a difference in a mean of 58.8 events and 48 events at 95% confidence. We
45
calculate two quantities for this test: the error given by N1/2 and the mean of 58.8 events.
Then to get to a 95% confidence upper bound on the Higgs production we would need to
collect 2.8 times as much data to place the same limits with a counting experiment as what
we do with the artificial neural network used in the 1.7 fb−1 analysis. So we do better than
a simple counting experiment.
7.1 Double SecVtx Tagged Events
The two tight SecVtx tagging category is one of two signal tagging regions. I ran the limit
calculations on these events to gauge the performance of the discriminant described in chapter
7. I expect the other tagging category with one tight SecVtx tag and one loose Jet Prob tag
will see comparable improvement. The limits were run with shapes coming from untagged
events because the statistics were much higher, and the shapes do not change sufficiently after
requiring tagging. The normalizations for the signal and background events came from the
two tight SecVtx tag numbers. Each limit was run on an independent sample to eliminate any
overtraining. In order to measure the improvement of the Global Discriminant, I compare
the results from the 1.7fb−1 neural network with the new global discriminant. Once the
cuts are loosened, the 95% Confidence Level Expected Limit for the 1.7fb−1 neural network
remains unchanged. In a direct comparison, the Global Expert Discriminant improves the
a priori limit by 14%, which can be seen in table 7.1. The 95% Confidence Level Expected
Limits are reported as the limit multiplied by the Standard Model expected cross-section,
and we want to see this limit approach one before we can say anything about the Higgs
production. The limit is analogous to asking how large would the Higgs cross-section have
46
Num
ber o
f Eve
nts
16
S/B ~ 1/7 in the last 2 bins
Figure 7.1: The expected shapes for the signal and background in the double SecVtx category.
to be in order for us to have observed it. This places an upper limit on how big the Higgs
cross-section can be. The shapes of the background and signal shapes can be seen in figure
7.1 above.
Table 7.1: 95% Expected Confidence Level Limits
Network Systematics Cuts Limits(∗SM Cross-section)
Old ANN 1.7fb−1 Yes Tight 10.2
Old ANN 1.7fb−1 No Tight 9.2
Old ANN 1.7fb−1 No Loose 9.2
Expert Discriminant No Loose 7.9
To compare the efficiency of each component of the ANN, I have done some comparisons
with different variable inputs. I trained an ANN with only the Individual Expert Discrimi-
nants and one with only the kinematic variables, and also I measured the performance of the
47
ANN used in the past analysis. The results of this work can be seen in table 7.2. The nor-
malizations in this table are a little different so that results in the difference in the numbers
that were presented in the previous table. However, we can still make direct comparisons
amongst these numbers. Then we see around a 13% from past ANN to the Global Dis-
criminant. Also there is also an improvement over simply giving the ANN more kinematic
variables, but this improvement falls short of the Global Discriminant by 9%. Adding the
5 important kinematic variables to the IEDs gives a 5% improvement, so that explains my
motivation for wanting to keep those variables in.
Table 7.2: 95% Expected Confidence Level Limits
Network Systematics Cuts Limits(∗SM Cross-section)
Old ANN 1.7fb−1 No Diff 6.8
IEDs only No Diff 6.2
10 Kinematic variables No Diff 6.5
Expert Discriminant No Diff 5.9
48
Chapter 8
Conclusions
The Expert Multivariate Technique results in a 14% improvement in the 95% confidence
level a priori expected statistical limit for the Higgs Boson in the ZH→ννbb analysis. The
quoted improvements are based on the improvement in events with two tight b tags. The
training for the all of the discriminants do not require any form of tagging for the events.
However, upon comparison of the shapes of the different backgrounds, the b tagging require-
ment causes no significant change in the shape of the backgrounds or signals. Hence, I expect
to see similar improvement with the other tagging selections. If this is the case, then then
one way to view the improvements is to say that we would have had to collect 30% more
data to see the same improvements with the old analysis technique.
As far as the systematic errors, I expect them to scale with the statistical improvements
as has been seen in past analyses. In the future, the increase in data will allow us to put
tighter constraints on the backgrounds, which decreases our systematic errors; therefore, the
systematic errors can change with the amount of data and in general decrease along with
statistical errors.
49
Some important features of the Expert Multivariate Technique is that it optimizes the
separation of each signal from each background individually. The Individual Expert Dis-
criminants allows for the selection of the most important distinguishing variables for each
background before training a Global Expert Discriminant. These separate trainings allow
the multivariate techniques to better account for the differences in the WH and ZH signals,
which was motivated by the differing performance of the ZH networks versus the WH net-
works. Since the Expert Multivariate Technique (EMT) optimizes the separation of each
background as well as incorporating the tracking information as another discriminant, it
reduces the total amount of background in the signal like region, which allows us to open
the cuts and accept more signal. The EMT deals with the extra background in a far more
effective way than the old 1.7 fb−1 neural network does.
Finally, the EMT is very general and does not require anything that is unique to the
ZH→ννbb channel; therefore, I believe that these ideas could fairly easily be extended to
other analysis like ZH→e+e−bb and WH→lνbb. I would expect to see similar increases
in sensitivity to the Higgs in these other channels. For example, the separation from the
tracking information could be used to improve the dijet mass resolution in the ZH→e+e−bb
analysis by getting a better gauge on some of the fake MET in the event. In this channel,
the information from the pair of electrons is used to apply a correction to the b jets, and the
correction improves the resolution of the dijet mass as well as the momentum and energy
of the jets. Other ideas for improvement are to investigate the use of a boosted decision
tree as the final discriminant instead of the Jetnet neural network. Also a check to see how
much improvement we get from just giving a boosted decision tree all of the variables is
important to show that the Individual Expert Discriminants are needed. Finally, I plan to
50
add in systematics as well as the other tagging categories. Most of these tests are in progress
and should be completed this summer.
The EMT improves our sensitivity to the Higgs boson, which is the simplest way of giving
particles in the Standard Model mass. It is important to find the Higgs because it can tell us
a lot about new physics. Also there is always the chance that the Higgs does not exist, which
poses an even more exciting proposition because it means that we really do not understand
the universe. Only time will tell whether the Higgs exists, but until then the Large Hadron
Collider will be starting up and will give us the opportunity to study the universe at a much
higher energy and on a grander scale.
51
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