Our physics problem consists in detecting the so-called “golden decay channel” $H \to ZZ^{*} \to l^{+}l^{-}l'^{+}l'^{-}$ 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's 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 $4\mu$ 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 ROOT File if prefer 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 $q\bar q' \to H q\bar q'\to ZZ^{(*)} q\bar q'\to 4\mu q\bar q'$ Image Added - our signal events - that we want to discriminate from the so-called Gluon Gluon Fusion $gg \to H \to ZZ^{(*)} \to 4\mu$ Image Added Higgs production events and the QCD process which are both irreducible backgrounds (you can see an example of an irreducible background in the Feynmann diagram at the leading order (LO) in the picture below and the cross-sections expected for the Higgs boson production processes and the branching ratios for its decay channels ).
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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.

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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 with $l$ Image Added)
particle jets (collimated streams of particles originating from quarks or gluons, denoted with $j$ Image Added).

For each object, several kinetic variables are measured:

the momentum transverse to the beam direction ( $pt$ Image Added)
two angles $\theta$ Image Added (polar) and $\phi$ Image Added (azimuthal) - see picture below for the CMS reference frame used.
for convenience, at hadron colliders, the pseudorapidity $\eta$ Image Added, defined as $\eta=-ln(tan(\eta/2))$ Image Added is used instead of the polar angle $\theta$ Image Added.