# Machine-Learning Application for a Likelihood Ratio Estimation Problem at LHC
## 3 Particle Physics Analyses Application
### YXH Fully-Hadronic Analysis  
The first analysis described is a search for a Beyond Standard Model (BSM) TeV-scale narrow-width boson Y decaying to a Standard Model Higgs (H) and a new O(100s) GeV-scale boson X [6]. The H is required to decay to \(b\bar{b}\), its largest branching ratio decay; explicit requests are not made for X, except that its decay products are jets. The full Large Hadron Collider Run 2 \(\sqrt{s}=13\) TeV \(pp\) dataset is used, collected by the ATLAS detector from 2015 to 2018 and corresponding to an integrated luminosity of 139 fb\({}^{-1}\). A Feynman diagram for this process is shown in Figure 1.  
Because H and X masses are of the order of thousands of GeV, they are created with a significant momentum component in the transverse plane with respect to the beam axis, labeled \(p_{T}\), that increases with the mass of the resonance. This collimates each boson's decay products, which are then reconstructed together as a single jet with a large radius, from now on, identified by J. Therefore, the signature of such a _signal_ is a resonant structure in the dijet invariant mass spectrum, where events can be selected based on a final state of two large-radius jets. A supplementary resolved selection is used to reconstruct the X mass with small-R jets (in this paper labeled with j) in the case of insufficient boost from the Y. The primary _background_ comprises SM multi-jet processes, where jets are produced from quantum chromodynamic [9] (QCD) interactions, producing a smoothly falling invariant mass distribution on top of which a signal bump can be isolated. Figure 1: Feynman diagram of the target _signal_ process, where the Y is produced in the initial \(pp\) collision and decays to a fully hadronic final state via an SM Higgs boson(\(\to b\bar{b}\)) and a new particle X. This search is motivated by several key extensions to the Standard Model, which predict heavy diboson resonances, one of the simplest being a simplified model based on spin-1 heavy vector triplets (HVT) [10], which reproduces a large class of BSM models. The final fit is performed on the reconstructed invariant mass of the Y in overlapping windows of the X candidate mass to further enrich the signal-to-background ratio. The results are presented as limits on the cross-section times branching ratio of the generic HVT process. SRs are constructed by selection based on the different properties of the H and X jets. An ambiguity resolution, required to determine which of the two J in the event is more likely to be the Higgs boson, is solved using a neural-net-based classifier, which separates bosons decaying to \(b\bar{b}\) from top quark and QCD jets [11]. The outputs of the NN are three classification scores corresponding to the likelihood of the jet originating from a Higgs boson (\(p_{Higgs}\)), top quark (\(p_{Top}\)), or multijet process (\(p_{multijet}\)), which are subsequently combined into the jet-level discriminant \(D_{X_{bb}}\), as shown in Equation (6). \[D_{X_{bb}}=\ln\frac{p_{Higgs}}{0.25\cdot p_{Top}+(1-0.25)\cdot p_{multijet}} \tag{6}\]  
The jet with the largest value of \(D_{X_{bb}}\) is labeled as the Higgs candidate (\(J_{H}\)), and the other J is, by default, the X candidate (\(J_{X}\)), therefore, determining which jet is subject to further H and X tagging. A novel anomaly detection _signal_ region is implemented based on a jet-level score for _signal_ model-independent tagging of the boosted X [12], representing the first application of fully unsupervised machine learning to an ATLAS analysis. The primary SR defined through a selection on the jet-level anomaly score (AS) of the X candidate is referred to as the _anomaly SR_. The remaining two SRs target the benchmark \(X\to q\bar{q}\) decay and are, thus, referred to as _two-prong SRs_, which differ based on reconstruction of the \(X\) as either a single large-R jet (_merged SR_) or two small-R jets (_resolved SR_).