Cosmological and astronomical observations show that most of the matter in the Universe is dark. This dissertation provides an overview of the dark matter evidence, and focuses on the particle dark matter hypothesis, describing possible particle candidates, concentrating on the Weakly Interactive Massive Particles (WIMPs). It describes the main WIMP detection strategies and addresses the subject of WIMP scattering in direct detection experiments. This work analyses the data from the XENON1T experiment, investigating within a Chiral Effective Field Theory (ChEFT) framework the nuclear recoils from possible WIMP interactions. It presents the XENON1T detector, the main backgrounds, the xenon signal emission model and the background studies, and describes the statistical inference adopted in the analysis.

The XENON1T detector was a dual-phase Time Projection Chamber (TPC) using a ~2 tonne liquid xenon target to detect scattering particles. WIMPs with masses above ~10GeV/c² scattering against the xenon nuclei would deposit enough energy to create an observable event.

The ChEFT analysis is performed on the XENON1T data from 278.8 days of operation for a total exposure of 1 tonne×year, with a combined likelihood of two science runs. The region of interest for this analysis was extended from [4.9, 40.9] keV_nr, in the Spin Independent analysis, to [4.9, 54.4] keV_nr, to increase the acceptance of possible models with rates peaking at higher energies (>0keV_nr). The analysis shows that the data is consistent with a background only hypothesis and provides constraints on the interaction coefficients and the physics scale for 25 different operators. The analysis is complemented by limits on three benchmark models of interaction using ChEFT. For these models we investigate the effect of isospin breaking interactions, reporting cancellation regions where the limit worsens up to 6 orders of magnitude with respect to the isospin conserving case.

The dissertation is complemented with the dark matter-electron scattering study within an EFT framework, analysing the single or few electron emission signals in XENON1T. The analysis provides the first experimental limits on the dark matter-electron effective operators for the magnetic and electric dipole, and anapole interactions.

Lastly, the dissertation describes an example of introducing a data-driven background model in an inference framework based on explicit multidimensional likelihood computation. The background modelling is done using calibration data from the XENONnT detector, the next iteration of a dual-phase xenon TPC in the XENON detector family, which is currently in operation.

The XENONnT experiment is a low-background dual phase liquid xenon Time Projection Chamber (TPC) with 5.9 tonnes of instrumented liquid xenon. Improved liquid xenon purification and radon distillation system along with various background mitigation strategies brought the Electronic Recoil (ER) backgrounds down to an unprecedented low of (15.8 ± 1.3) events/(keV tonne years) below recoil energies of 30 keV.

Exploring three different ER datasets spanning 10 to 140 keV collected using the XENON1T and XENONnT detector, a search for a signal of sub-GeV Dark Matter boosted by reflection off the sun is conducted. No excess is observed, and novel stringent upper limits on the Dark Matter-electron scattering cross section in the Dark Matter mass range between 5 keV and 9 MeV are reported.