In this thesis the linearity of the ATLAS track-counting luminosity measurement is studied using two different sets Monte Carlo simulated crossings of proton-proton bunches. A primary high-momentum, or hard, interaction must be chosen for the Monte Carlo simulation. The first of the two sets is simulated using Z→µµ as primary hard scatter in the bunch crossings while the second set is simulated with a single neutrino particle gun as the primary hard scatter. The luminosity can be determined by track counting from the relationship between the number of reconstructed charged particle tracks and the number of proton-proton interactions per bunch crossing in the ATLAS detector. The relationship between the two is theoretically linear but is affected by non-linear effects from the presence of fake tracks and the reduced tracking efficiency at large µ.  The linearity is studied and compared for eight different sets of track selection criteria called working points. Four of the working points were used during Run 2 of the Large Hadron Collider and four are introduced for Run 3.  It is found that the use of the physical hard scatter, Z→µµ, in the Monte Carlo generation results in the appearance of tracks at all interaction rates, to a degree that does not agree with experiment. The use of the single neutrino particle gun for the simulation of hard scatter interactions is found to be more suitable for the track counting studies. Two of the working points introduced for Run 3, called TightModHighPtStrictLumi and TightModFullEtaHighPtStrictLumi, are found to outperform the rest of the working points. / I denna uppsats studeras linjäriteten av en luminositet-mätningsmetod kallad track-counting som används vid ATLAS-detektorn. Linjäriteten studeras för två olika uppsättningar av simulerade proton-protonkollisioner. Kollisionerna produceras med hjälp av Monte Carlo-simuleringar. Den första uppsättningen simuleras användandes Z→µµ som mest högenergetisk interaktion i alla event medan den andra uppsättningen istället simuleras användandes en högenergetisk neutrinopartikel i alla event. Med hjälp av track-counting bestäms luminositeten genom förhållandet mellan antalet rekonstruerade laddade partikelspår och antalet proton-protoninteraktioner per "bunch crossing" i ATLAS-detektorn. I teorin är relationen mellan de två linjär, men track-counting metoden påverkas av icke-linjära effekter såsom falskt rekonstruerade partikelspår och minskad effektivitet vid stora µ-värden. Linjäriteten studeras och jämförs för åtta olika uppsättningar av kriterier som appliceras på partikelspåren. Linjäriteten jämförs for åtta olika uppsättningar av spårkriterier som kallas "Working points". Fyra Working points har tidigare använts under den andra körningen av "the Large Hadron Collider" medan fyra Working points är introducerade inför den tredje körningen.   Användningen av uppsättningen kollisioner som simuleras med Z→µµ som mest högenergetisk interaktion resulterar i spår vid alla µ-värden till en grad som inte överensstämmer med förväntningar. Användningen av neutrinopartikeln som mest högenergetsik interaktion vid simulering av event visar sig vara mer lämplig för studier som berör track-counting. Två av de Working points som introducerades inför den tredje körningen av "The Large Hadron Collider" visar sig prestera bättre än de andra. Dessa Working points har namnen TightModHighPtStrictLumi och TightModFullEtaHighPtStrictLumi.

This licentiate thesis presents contributions to the luminosity measurement from the data recorded by the ATLAS detector in 2017 using a track-counting technique, as well as a search for dark matter in the ATLAS experiment using 139 fb-1 of √s = 13 TeV pp collision data delivered by the LHC from 2015 to 2018. Track-counting luminosity measurements in low-luminosity operations are performed to study the effect of low collision rates on luminosity determination. The luminosity measured in a calibration transfer procedure using the track-counting technique is used to correct the pile-up dependence observed in ATLAS’s main luminosity detector called LUCID. A search in the final state of a lepton, jets and missing transverse energy, where the final state is produced from a pair of top quarks and a spin-0 scalar/pseudoscalar mediator, is presented. A dedicated signal region is designed to target this final state in which the mediator decays into dark matter particles. The signal region covers the search in the mass plane of the mediator and the dark matter particle. Dedicated control regions are designed to estimate the top-quark background events, as well as the events where a Zboson is produced in association with the top quarks. The signal region event counts in the data have not been unblinded yet, but expected exclusion limits at 95% confidence level as a function of mediator mass are presented. Scalar and pseudoscalar mediators are expected to be excluded up to 200 and 250 GeV, respectively, for the dark matter mass of 1 GeV, and the coupling strengths of the mediator to the dark matter and Standard Model particles of 1.