# Machine-Learning Application for a Likelihood Ratio Estimation Problem at LHC
## 3 Particle Physics Analyses Application
### Resonant HH in the bbbb Final State  
The second ATLAS analysis described in this paper, which adopted the same _background_ estimation technique, is a search for resonant (in particle physics, the term _resonant_ stands for processes having a peaked invariant mass distribution around the mass of a particle which has decayed into the observed final state) Higgs boson pair production in the \(b\bar{b}b\bar{b}\) final state [7]. LHC \(pp\)-collisions data collected by ATLAS in 2016-2018 are used, corresponding to \(126\ fb^{-1}\). To perform the search, a selection of the events used is performed, according to the expected properties of the signal, and _signal_ and _control regions_ are defined. The considered hadronic final state is explored by selecting only events with at least four small-R jets. Then kinematic cuts are applied to obtain SRs and CRs for the final fit on the 4\(\mathrm{b}\) invariant mass distribution, summarized as follows: Events are first divided into two categories: \(2b\), where exactly two jets are b-tagged (a b-tagged jet is a jet identified as produced by the hadronization of a b quark) and \(4b\), where at least four jets are b-tagged. Exactly four jets are selected to construct the two H candidates. For 4\(\mathrm{b}\) events, the four b-tagged jets with the highest \(p_{T}\) are selected. For \(2b\) events, the two b-tagged jets and the two untagged jets with the highest transverse momentum are selected. The \(2b\) events are needed to construct the _background_ model for the \(4b\) category. This selection of untagged jets can introduce a kinematic bias with respect to the \(4b\) category; however, this is exactly what is accounted for by the reweighting function. After the four jets are chosen, they are paired to form the two Higgs candidates H\({}_{1}\) and H\({}_{2}\) and the pairing is chosen by a boosted decision tree (BDT). Pairs are then ordered in terms of their transverse momentum. The multi-jet _background_ is reduced by requiring a certain angular separation between the two H candidates; processes coming from the top decay are suppressed by a proper applied veto. Finally, events are sorted into three kinematic regions based on the invariant masses of the H candidates: a _signal region_ (SR), a _validation region_ (VR) and a _control region_ (CR). Background Estimation  
After the selections described above, the _background_ is mainly composed of pure QCD multi-jet processes; therefore, the discussed data-driven technique fits the _background_ estimation problem well. Since the _signal_ contamination in the \(2b\) region is found to be negligible compared to the _background_ uncertainties, these data are used to predict the background_ shape in the \(4b\) SR. As in the previously discussed analysis, the HSB of the Higgs mass window is used for the training of the neural network; in this case, the CR plays the same role. Here a reweighting function is approximated by data to map the \(2b\) kinematic region onto the \(4b\) region. This function is then applied to the corresponding \(2b\) SR in order to have a _background_ model in the \(4b\) SR. The neural network used to minimize the loss in Equation (5) is composed of three densely-connected hidden layers, with 50 nodes and a ReLU activation function each, and an output layer with a single neuron with a linear activation function. The variables used in the input to the NN for training performed in CR are chosen to be sensitive to the differences between the two kinematic regions.