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and it must learn how to classify new datasets (the test dataset in our case).
This means that we have the same set of features (random variables) with their own distribution on the H0 and H1 hypotheses.
To obtain a good ML classifier with high discriminating power, we will follow the following steps:
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Particle Physics basic concepts: the Standard Model and the Higgs boson
The Standard Model of elementary particles represents our knowledge of the microscopic world. It describes the matter constituents (quarks and leptons) and their interactions (mediated by bosons), which are the electromagnetic, the weak, and the strong interactions.
Among all these particles, the Higgs boson still represents a very peculiar case. It is the second heaviest known elementary particle (mass of 125 GeV) after the top quark (175 GeV).
The ideal tool for measuring the Higgs boson properties is a particle collider. The Large Hadron Collider (LHC), situated nearby Geneva, between France and Switzerland, is the largest proton-proton collider ever built on Earth. It consists of a 27 km circumference ring, where proton beams are smashed at a center-of-mass energy of 13 TeV (99.999999% of the speed of light). At the LHC, 40 Million collisions / second occurs, providing an enormous amount of data. Thanks to these data, ATLAS and CMS experiments discovered the missing piece of the Standard Model, the Higgs boson, in 2012.
During a collision, the energy is so high that protons are "broken" into their fundamental components, i.e. quarks and gluons, that can interact together, producing particles that we don't observe in our everyday life, such as the Higgs boson. The production of a Higgs boson via a vector boson fusion (VBF) mechanism is, by the way, a relatively "rare" phenomenon, since there are other physical processes that occur way more often, such as those initiated by strong interaction, producing the Higgs boson by the so-called gluon-gluon fusion (ggH) production process. In High Energy Physics, we speak about the cross-section of a physics process. We say that the Higgs boson production via the vector boson fusion mechanism has a smaller cross-section than the production of the same boson (scalar particle) via the ggH mechanism.
The experimental consequence is that distinguishing the two processes, which are characterized by the decay products, can be extremely difficult, given that the latter phenomenon has a way larger probability to happen. In the exercise, we will propose to merge different backgrounds to be distinguished from the signal events.
Experimental signature of the Higgs boson in a particle detector
Let's first understand what are the experimental signatures and how the LHC's detectors work. As an example, this is a sketch of the Compact Muon Solenoid (CMS) detector.
A collider detector is organized in layers: each layer is able to distinguish and measure different particles and their properties. For example, the silicon tracker detects each particle that is charged. The electromagnetic calorimeter detects photons and electrons. The hadronic calorimeter detects hadrons (such as protons and neutrons). The muon chambers detect muons (that have a long lifetime and travel through the inner layers).
Our physics problem consists of detecting the so-called golden channel
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H→ ZZ*
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→ l+ l- l'+ l'- which is one of the possible Higgs boson's decays: its name is due to the fact that it has the clearest and cleanest signature of all the possible Higgs boson decay modes. The decay chain is sketched here: the Higgs boson decays into Z boson pairs, which in turn decay into a lepton pair (in the picture, muon-antimuon or electron-positron pairs). In this exercise, we will use only datasets concerning the 4mu decay channel and the datasets about the 4e channel are given to you to be analyzed as an optional exercise. At the LHC experiments, the decay channel 2e2mu is also widely analyzed.
Data exploration
In this exercise we are mainly interested in the following ROOT files (you may look at the web page ROOT file if you would like to learn more about which kind of objects you can store in them):
- VBF_HToZZTo4mu.root;
- GluGlueHtoZZTo4mu.root;
- ZZto4mu.root.
The VBF ROOT file contains the Higgs boson production (mass of 125 GeV) via the Vector Boson Fusion (VBF) mechanism (qqH) signal events - that we want to discriminate from the so-called Gluon Gluon Fusion (ggH) Higgs production events and the QCD process ZZ → 4mu which are both irreducible backgrounds (see the Feynmann diagram in the pictures and the cross-sections/branching ratios expected for Higgs boson production processes and its decay channels).
The processes are characterized by the same final-state particles but we can use the value of multiple variables, such as kinematic properties of the particles, for classifying data into the two categories, signal, and background. The first one is the statistically less probable process that results in producing the Higgs boson at the Large Hadron Collider (LHC) experiments and it is still understudies by the CMS collaboration.
In order to train our Machine Learning algorithms, we will look at the decay products of our physics problem. In our case we going to deal with:
- electrically-charged leptons (electrons or muons, denoted l)
- particle jets (collimated streams of particles originating from quarks or gluons, denoted j).
For each object, several kinetic variables are measured:
- the momentum transverse to the beam direction pt
- two angles θ (polar) and φ (azimuthal) - see picture below for the CMS reference frame used
- for convenience, at hadron colliders, the pseudorapidity η, defined as η =-ln(tan(η/2)) is used instead of the polar angle θ.
We will use some of them for training our Machine Learning algorithms.
How to execute it
Use Googe Colab
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