Measurement of $ZZ$ production and search for anomalous neutral triple gauge couplings in $pp$ collisions at $\sqrt{\textbf{s}}=$ 13 TeV with the ATLAS experiment

The study of boson pair production in proton-proton ($pp$) interactions at the Large Hadron Collider (LHC) gives the opportunity to test the electroweak sector of the Standard Model and search for new physics at highest available energies. One of these processes is the production of two $Z$ bosons, which is also a dominating background for analyses studying the decay of the Higgs boson to two $Z$ bosons. A measurement of $ZZ$ production in the $\ell^{+}\ell^{-}\ell '^{+} \ell '^{-}$ $(\ell,\ell' = e,\mu)$ decay channel is presented in this thesis. Data of $pp$ collisions at $\sqrt{s}=13$ TeV which was collected by the ATLAS experiment is used. The amount of collected data from 2015 and 2016 corresponds to an integrated luminosity of 36.1 $\text{fb}^{-1}$. Selected data is compared to simulations for on-shell $Z\rightarrow \ell^+ \ell^-$ candidate masses in the range of 66 GeV to 116 GeV and used to extract differential and integrated cross sections. The cross sections are corrected for detector effects and measured in a fiducial phase space corresponding to the detector acceptance. The differential cross sections are provided as functions of seven observables, including some that describe the jet activity in the event. Analyzing $ZZ$ events with additional jets is particularly important to study properties of higher order QCD corrections. The integrated cross section is also extrapolated to a total on-shell phase space and all $Z$ boson decay modes in the Standard Model using simulations. The resulting cross section is $17.3 \pm 0.9 [\pm 0.6 $(stat.)$\pm 0.4 $(syst.)$\pm0.6 $(lumi.)$]$ pb, which is in good agreement with Standard Model predictions. The production of two $Z$ bosons can also be used to search for neutral triple gauge boson couplings which are forbidden in the Standard Model. The high center of mass energy of the LHC is a perfect environment to search for such phenomena which are expected to be located predominantly at high energies. High tails of the transverse momentum distribution of the leading $Z$ boson candidate are analyzed for deviations between the Standard Model expectation and data. No significant differences are found. Therefore 95% C.L. limits on four different anomalous coupling parameters are set using two different parameterizations. The currently best limits extracted from ATLAS data on anomalous couplings using a vertex parameterization are: $-0.0018 < f_4^\gamma < 0.0018$, $-0.0018 < f_5^\gamma < 0.0018$, $-0.0015 < f_4^Z < 0.0015$, $-0.0015 < f_5^Z < 0.0015$. For the first time also following limits are set on dimension 8 operators using an effective field theory parameterization: $-5.9$ TeV$^{-4}<$ $C_{\tilde{B}W}/\Lambda^{4}<5.9$ TeV$^{-4}$, $-3.0$ TeV$^{-4}<$ $C_{WW}/\Lambda^{4}<3.00$ TeV$^{-4}$, $-3.3$ TeV$^{-4}<$ $C_{BW}/\Lambda^{4}<3.3 $TeV$^{-4}$, $-2.7$ TeV$^{-4}<$ $C_{BB}/\Lambda^{4}<2.8 $TeV$^{-4}$.