First observation of the associated production of $Z$ bosons with prompt and non-prompt $J/\psi$ mesons in $pp$ collisions at $\sqrt{s}= 8\,\mathrm{TeV}$ and contribution to the Micromegas detectors for the New Small Wheel upgrade of the ATLAS experiment

The associated production of vector boson with heavy quarkonia is a key observable for understanding the quarkonium production mechanism. This thesis studies the production of $J/\psi$ mesons in association with $Z$ bosons, using $pp$ collision data at $\sqrt{s}=8\,\mathrm{TeV}$ collected with the ATLAS experiment at the LHC. Since the $J/\psi$ meson can be produced in the experiment either by prompt QCD processes or by a subsequent decay of a $b$-hadron (having longer lifetimes than prompt), both $Z+$ prompt $J/\psi$ and $Z+$ non-prompt $J/\psi$ productions are examined. The associated production rate of $Z+$ prompt (or non-prompt) $J/\psi$ is measured as a function of the inclusive $Z$ production. The decay modes chosen for this study were the $Z\to\ell^+\ell^-$, where $\ell=\mu,e$ and $J/\psi\to\mu^+\mu^-$. In order to correct for the muon reconstruction inefficiency of the $J/\psi$ muons (the $Z$ decay products reconstruction efficiency cancels in the ratio), the muon reconstruction efficiency of the ATLAS experiment is measured using the tag-and-probe method with $J/\psi\to\mu^+\mu^-$ decays. The two final state particles, $Z$ and $J/\psi$, may occur from either a single pair of interacting partons (single parton scattering) or two pairs of partons (double parton scattering). The contribution from double parton scattering is examined and subtracted in order to compare the measurement with theory calculations. Colour singlet theoretical models predicted that this process could not be observed with the data collected from the LHC during $2012$, while colour octet models calculated a handful of events. From the result of the measurement, CO models underestimate the data by a factor $5$ in the high-$p_\mathrm{T}$ region. The double parton scattering effective cross-section ($\sigma_\mathrm{eff}$) is considered to be process independent and slightly correlated with $\sqrt{s}$. The azimuthal angle observable between the $Z$ and the $J/\psi$ being sensitive to double parton scattering is used to derive a lower limit on $\sigma_\mathrm{eff}$. This was the first information on $\sigma_\mathrm{eff}$ for $\sqrt{s}=8\,\mathrm{TeV}$. Furthermore, the search for the $B_s\to\mu^+\mu^-$ is presented. For this rare process, the separation of the signal to background is described as well as the extraction of the $B^\pm\to J/\psi K^\pm$ reference channel, used in the cross-section measurement. Looking towards the future and the upgrades of the ATLAS experiment, this thesis studies the micromegas detector as part of the new small wheel. It presents its main characteristics in terms of efficiency and performance, derived from test-beam studies and from data collected from micromegas placed in the ATLAS cavern.