Measurements of the Higgs cross section and inclusive ZZ lineshape using 4$\ell$ final state with the ATLAS experiment

The physics analyses presented in this dissertation use four-lepton (4$\ell, ~\ell = e, \mu$) final state to measure the Higgs boson to $ZZ$ coupling, and the inclusive $ZZ$ production lineshape with data collected by the ATLAS experiment in the proton-proton collisions of the Large Hadron Collider (LHC) at a center-of-mass energy of $ \sqrt{s} = 13~{Te\kern -0.1em V}$. The first analysis presented is the Higgs boson production cross section measurement in reaction of $H \rightarrow ZZ^* \rightarrow 4\ell$. The 4$\ell$ final state has the highest signal to background ratio compared to all other Higgs decay channels, thus it is ideal for precision measurement of the Higgs properties. The analysis uses the full Run 2 dataset, corresponding to an integrated luminosity of 139 $fb^{-1}$. The Higgs boson production mode and kinematic variables are used to categorize the selected Higgs events both at fiducial and the reconstructed level under the latest Simplified Template Cross Section(STXS) framework to reduce the dependence on uncertainties of theoretical modeling. In each of the signal category in the Higgs mass window with enough statistics, multivariate analysis is performed to further separate Higgs signal from different production modes and the Standard Model (SM) background. The output discriminant is used as the observable in the simultaneous fit to extract the Higgs boson production cross section. Furthermore, several new categories are optimized in the Higgs mass side-band region to constrain SM background from data. The inclusive cross section times branching ratio over the SM prediction in the Higgs production rapidity range, $|y_H| < 2.5$, is measured to be \begin{equation*} {(\sigma\cdot \mathcal{B}) / (\sigma\cdot \mathcal{B})_{\mathrm{SM}}}= 1.01 \pm 0.09, \end{equation*} which marks a very good agreement between data and the SM prediction. The second analysis presented is the lineshape measurement of invariant mass spectrum of four-lepton system using data collected during 2015 and 2016, corresponding to an integrated luminosity of 139 $fb^{-1}$. The differential distribution of $m_{4\ell}$ and several two-dimensional distributions of $m_{4\ell}$ vs secondary variables, including a Matrix Element discriminant ``MELA'' for the off-shell Higgs extraction, are measured with optimized binning for proper migration and high purity. The unfolding method used in the measurement is optimized with pseudo-experiments to make a balance between statistical uncertainty and residual bias. The unfolding process is validated with the standard unfolding closure test. The differential cross sections of the measurement are consistent with SM calculations. The results are then interpreted and tested against different 4$\ell$ production models, including the quark pair and the gluon-gluon fusion initial states. The $gg \to ZZ^{*}$, gluon-originated signal strength is measured to be $1.32^{+0.45}_{-0.45}$. This result is based on theoretical calculation of the $gg \to ZZ^{*}$ production with the QCD next-to-leading order (NLO) correction, and it indicates higher order correction in calculation is necessary to understand the source of the $4\ell$ production mechanism. A 95% confidence level upper limit of $6.5$ is set on the off-shell Higgs signal strength with the $m_{4\ell}$ - MELA distribution using the CL$_s$ statistical approach. The branching ratio of $Z\to4\ell$ is measured in a phase space of $80 < m_{4\ell} < 100\ Ge\kern -0.1em V$ and $m_{\ell\ell} > 4\ Ge\kern -0.1em V$ as: \begin{equation*} \mathcal{B}_{Z\rightarrow4l} = \left(4.70 \pm 0.32 (\text{stat.}) \pm 0.21 (\text{sys.}) \pm 0.03 (\text{theo.}) \pm 0.14 (\text{lumi})\right)\times 10^{-6} . \end{equation*} Finally, a 95% confidence level CL$_s$ exclusion contour is set on modified Higgs coupling parameters ($c_t$, $c_g$) in a Higgs effective field theory.