Search for the Vector Boson Scattering in W$^{+}$W$^{-}$ -> 2l2$\nu$ final state with the CMS detector

My PhD research activity has been carried out within the CMS collaboration and is focused on data analysis. The CMS experiment is one of the main detectors installed at the Large Hadron Collider (LHC) at CERN, in Geneve, and is a multi-purpose apparatus in the context of high energy physics. During my PhD course in Physics and Astrophysics I have been working on the observation of electroweak W$^{+}$W$^{-}$ pair production in association with two jets in proton-proton collisions at $\sqrt{s}=13$ TeV, and the paper has been published by the PLB journal. This process belongs to the so-called Vector Boson Scattering (VBS) mechanisms: broadly speaking, the set of VBS processes involve scattering diagrams among gauge vector bosons, i.e. VV $\rightarrow$ VV amplitudes with V being either a W, Z or gamma boson. At the LHC, they manifest in association with two hadronic jets, coming from the interacting quarks that take part in the proton-proton collision. My thesis presents the first observation of the electroweak (EW) production of a W$^{+}$W$^{-}$ bosons pair. The analysis is based on the full Run 2 data set collected by the CMS experiment and corresponding to an integrated luminosity of 138 fb$^{-1}$. Signal candidates must pass either single or double lepton triggers, as both W bosons are required to decay into a light lepton - electron (e) or muon ($\mu$) - along with its corresponding neutrino. Moreover, two VBS-like jets are selected, i.e. tight kinematic cuts on the dijet invariant mass ($m_{jj}$) and pseudorapidity gap ($\Delta\eta_{jj}$) are applied to the two jets with the highest transverse momentum ($p_{T}$) in the event. To achieve a better sensitivity to the VBS signal process, both different- and same-flavor final states are considered for this analysis, which, combined together, have enough statistical power to make the observation possible. Indeed, the main challenges of this analysis are the background estimation and reduction techniques, which are fundamental ingredients for measuring such a rare process. Unlike other VBS modes, the W$^{+}$W$^{-}$ channel is populated by the top-antitop quark (ttbar) pair production background, which represents the main background source for its huge cross section: a Deep Neural Network (DNN) algorithm is used to disentangle this background and the QCD-induced W$^{+}$W$^{-}$ production from the VBS signal in emu categories. On the other hand, ee and $\mu\mu$ final states are dominated by Drell-Yan (DY) events, in which jets from secondary interactions, i.e. pileup jets, fake the real source of transverse missing momentum ($p_{T}^{miss}$) that one would expect from the emission of neutrinos. A dedicated strategy is developed to measure this background process, and the $m_{jj}$ variable has enough discriminating power in ee and $\mu\mu$ categories. The statistical significance of the EW W$^{+}$W$^{-}$ production is 5.6 standard deviations with respect to the background-only hypothesis (5.2 expected). Two fiducial cross section measurements are quoted for this process, one being more inclusive, as it represents the cross section measured in the phase space where the signal sample has been generated, and the other one being closer to the experimental selection outlined at reconstruction-level. The measured (expected) value is $99 \pm 20$ fb for the former and $10.2 \pm 2.0$ fb for the latter, and they are both in agreement with leading order QCD predictions: $89 \pm 5$ fb and $9.1 \pm 0.6$ fb, respectively. Future data taking periods of the LHC will enable further precision studies in the context of VBS measurement, from the Run 3 - which has just started - to the upcoming high luminosity phase, which will allow to collect more than 3000 fb$^{-1}$ of new data. In this landscape, differential cross section measurements and combinations of multiple diboson VBS channels will play a key role in understanding the physics of these rare EW processes, possibly pointing to new physics phenomena that governate laws of nature in the realm of high energy interactions.