Physics with $b$-jets using the ATLAS Run 2 data: from calibration to Higgs boson couplings measurements in the $VH,H\to b\bar{b}$ channel

Many signatures of interest for Standard Model (SM) measurements and for searches of beyond-SM (BSM) phenomena include at least one $b$-jet in their final state. For instance, the main decay of the Higgs boson ($H$) is to a pair of $b$-quarks with a SM predicted branching fraction of 58%. The Higgs boson is the cornerstone particle of the SM as it is responsible for the mass of the other elementary particles and for the spontaneous symmetry breaking of the electroweak interaction. $H\to b\bar{b}$ decays are thus essential to probe the quark mass generation mechanism and constrain BSM theories in the Higgs sector. Moreover, other processes such as top-quark production and heavy flavour decays of $Z$ boson or of hypothetical new resonances can produce $b$-jet(s). This thesis focuses on calibration and physics measurements of processes involving $b$-jets exploiting proton-proton collisions collected at a center-of-mass-energy of 13 TeV between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider. The first aspect of the thesis work concerns the first ATLAS in situ differential calibration of the energy scale of $b$-jets, referred to as $b$-JES. Events with a $t\bar{t}$ lepton+jets signature are selected and the $b$-JES is derived thanks to a new software framework developed for that purpose. The $b$-JES measurement has been performed inclusively for $b$-tagged jets transverse momenta above 20 GeV, and thanks to the large size of the control sample under study, differentially as a function of the $b$-tagged jet transverse momentum between 30 and 500 GeV. The specific $b$-tagged jet energy correction in data is consistent with unity, with an uncertainty of 2.5% for the inclusive measurement, and decreasing from 4% to 1.9% for $b$-tagged jet transverse momenta increasing between 30 and 500 GeV for the differential measurement. The results have been published in a dedicated ATLAS conference note and have been presented at the Moriond Electroweak 2022 conference during a YSF talk session. The second part of the thesis is about a study of the properties of the Higgs boson. The Higgs-to-bottom Yukawa coupling, the SM predictions and kinematic properties of Higgs boson production are probed looking for Higgs bosons produced in association with a weak vector boson ($V=W,Z$) and decaying to a pair of $b$-quarks. The vector bosons are reconstructed through their leptonic decays. The $V(\to \mathrm{leptons})H(\to b\bar{b})$ final state provides the best sensitivity to the measurement of the $VH$ production cross-section and the $H\to b\bar{b}$ decay rate. Thanks to improved $b$-jet and $c$-jet identification algorithms and other refinements in the analysis procedures such as a more extensive use of multivariate techniques, an increase of the order of 20% of the sensitivity is expected for the $VH,H\to b\bar{b}$ analysis with respect to the previous ATLAS publication based on the same data. The expected precision on the signal strength, defined as the ratio between the observed signal yield and the corresponding SM prediction, is equal to $\mu_{VH}^{H\to b\bar{b}} = 1.00^{+0.15}_{-0.14}$. Furthermore, the expected 95% confidence level upper limit on the signal strength of the $VH,H\to c\bar{c}$ process is expected to be of 16 times the prediction of the Standard Model and is a factor 2 lower than in the previous published analysis of the same data. A publication of those results is foreseen for the end of 2023.