Measurement of differential and integrated fiducial cross sections for Higgs boson production in the four-lepton decay channel in pp collisions at $\sqrt{s} = 7, 8$ and $13$~TeV

Integrated fiducial cross sections for the production of four leptons via the $H \rightarrow 4\ell$ decays ($\ell = e, \mu$) are measured in pp collisions at $\sqrt{s} = 7, 8$ and $13$~TeV. Measurements are performed with data corresponding to integrated luminosities of 5.1 fb${}^{-1}$ at $\sqrt{s}=7$~TeV, 19.7 fb${}^{-1}$ at $\sqrt{s}=8$~TeV and 12.9 fb${}^{-1}$ at $\sqrt{s}=13$~TeV, collected with the CMS experiment at the LHC. Differential cross sections are measured as a function of transverse momentum of four-lepton system and accompanying jet multiplicity using 8 and 13~TeV dataset. All cross sections are measured within a fiducial phase space defined by the requirements on lepton kinematics and event topology. The integrated $H \rightarrow 4\ell$ fiducial cross section is measured to be $0.56^{\rm +0.67}_{\rm -0.44} \, {\rm(stat.)}\, ^{\rm +0.21}_{\rm -0.06}\, {\rm (sys.)} \, \pm{0.02}\, {\rm (model)}\, {\rm fb}$ at 7 TeV, $1.11^{\rm +0.41}_{\rm -0.35} \, {\rm(stat.)}\, ^{\rm +0.14}_{\rm -0.10}\, {\rm (sys.)} \, ^{+0.08}_{-0.02}\, {\rm (model)}\, {\rm fb}$ at 8 TeV and $2.29^{+0.74}_{-0.64}({\rm stat.})^{+0.30}_{-0.23}({\rm sys.})^{+0.01}_{-0.05}({\rm model})$fb at 13 TeV. The measurements are found to be compatible with the theoretical calculations based on the standard model.