Measurements of properties of the Higgs boson in the four-lepton final state in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

Properties of the Higgs (H) boson are measured in the $\mathrm{H}\rightarrow{\rm Z}{\rm Z}\rightarrow4\ell$ ($\ell={\rm e},\mu$) decay channel. The full data sample of proton-proton collisions at a center-of-mass energy of $13~\mathrm{TeV}$ is used, corresponding to an integrated luminosity of $137.1~\mathrm{fb}^{-1}$ recorded in 2016, 2017, and 2018 by the CMS detector at the LHC. The signal-strength modifier $\mu$, defined as the ratio of the H boson rate in the $4\ell$ channel to the Standard Model (SM) expectation, is measured to be $\mu=0.94^{+0.07}_{-0.07}({\rm stat.}) ^{+0.08}_{-0.07}({\rm syst.})$ with the H boson mass profiled in the fit. The signal-strength modifiers for different H boson production modes are also constrained. Measurements of the simplified template cross sections, designed to quantify the different H boson production processes in specific regions of phase space, are reported. The cross section for the production of the $\mathrm{H}\rightarrow4\ell$ in a fiducial region closely matching the experimental selection of the leptons is measured to be $\sigma_{{\rm fid.}}=2.73^{+0.23}_{-0.22}({\rm stat.})^{+0.24}_{-0.19}({\rm syst.})~{\rm fb}$ at $m_{\rm H} = 125.09~\mathrm{GeV}$, compared to a SM prediction of $2.76 \pm 0.14~\mathrm{fb}$. Differential cross sections as a function of the $p_{\rm T}$ and rapidity of the H boson, the number of associated jets, and the $p_{\rm T}$ of the leading associated jet are determined. All results are found to be compatible with the SM predictions, within the measurements precision.