Investigating the nature of dark matter and of the Higgs boson with jets and missing transverse momentum at the LHC

Dark matter (DM) is one of the outstanding questions to which the Standard Model of particle physics (SM) still has no answer. Indeed, numerous evidences point to the existence of a non-baryonic matter component in the Universe that interacts with ordinary matter only through gravity. Under the hypothesis of the existence of a new interaction, three types of searches have been developed, among them collider searches represent a promising way of discovering and characterizing the properties of dark matter. In this thesis, the search for DM is carried out in final states where a highly-energetic hadronic jet recoils against a large missing transverse momentum. The latter would be the signature of the production of weakly-interacting particles, which can be tagged in the final states thanks to the emission of radiation from the initial state of the collisions. The results were obtained with the data collected by the ATLAS experiment during the Run2 of the LHC, corresponding to 139 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV. The main SM background of the presented search, also called $monojet$ search, is the $Z(\rightarrow \nu\bar{\nu})$+jets process, which has the same signature as the searched signal. A semi-data-driven technique is used to correct the Monte Carlo (MC) background predictions using data in independent control regions. Together with the adoption of accurate predictions for SM $W/Z$+jets processes, the background estimation technique allows to reduce the uncertainty of SM predictions to the percent range. The results presented in this thesis are interpreted in simplified DM models and compressed SUSY scenarios. The monojet analysis is also used to study the properties of the Higgs boson. An upper limit is set on its branching fraction into invisible final states, and the parameters of models that foresee the production of long-lived particles (LLPs) in its decay are also constrained. Final states with jets and missing transverse momentum can also be produced by the decay of a Higgs boson into a $b\bar{b}$-pair, if the Higgs boson is produced in association with an invisibly-decaying $Z$-boson. The $Z(\nu\bar{\nu})H(b\bar{b})$ process is one of the leptonic channels of the $V(\rightarrow \textit{lep.})H(b\bar{b})$ process, where $V$ can be either a $W$ or $Z$ boson. This allows the $H(b\bar{b})$ decay mode to be studied by exploiting the leptons to trigger and identify the events. The ATLAS collaboration has published two results with the full statistics collected during LHC Run 2, studying the $VH(b\bar{b})$ process in both well-resolved and boosted $H\rightarrow b\bar{b}$ decays. However, the two analyses are not statistically independent and rely on preliminary particle reconstruction and identification techniques. In this thesis, the work towards a Run 2 legacy result is presented, based on state-of-the-art reconstruction algorithms and an optimal combination of the two kinematic regimes. The performance of flavour tagging with new jet reconstruction algorithms is presented, along with an innovative method, based on graph-neural-networks, for performing an event-weighting technique called \textit{truth tagging}, which helps to reduce systematic uncertainties due to limited Monte Carlo statistics. Finally, a first fiducial differential cross-section measurement of the $H(b\bar{b})+$\met~process is presented. This result forms the basis for more complete and refined work that will be included in the Run 2 Legacy result on the $VH(b\bar{b})$ process by the ATLAS collaboration. The leading background process of the two analyses presented in this thesis is the production of a leptonically-decaying $W$ or $Z$ boson in association with hadronic jets. In the final part of the thesis, the implication of recent developments in the \sherpa~MC event generator for ATLAS analyses are presented. The impact on the modelling of physical quantities thanks to the improvements of the matrix element and parton shower models is presented. The effect of changes in the description of the production fractions of heavy-flavour-hadrons is shown, and the performance of a preliminary setup based on the \emph{fusing} of a $Z+bb$ calculation done in a four number-of-flavours scheme (NFS) with the inclusive 5NFS $Z$+jets calculation is presented. In addition, the performance of a technique for generating events based on the bias of the cross-section is discussed, and the studies leading to the final configuration adopted by the ATLAS collaboration for the generation of $V$+jets events are presented.