Measurement of inclusive and differential fiducial cross sections of Higgs boson production in the H$\rightarrow 4\ell$ decay channel in proton-proton collisions at 7~TeV and 8~TeV

In this document we present measurements of inclusive and differential fiducial cross sections of the Higgs boson production in proton-proton collisions with integrated luminosities of 5.1 fb${}^{-1}$ at $\sqrt{s}=7$~TeV and 19.7 fb${}^{-1}$ at $\sqrt{s}=8$~TeV using the $H \rightarrow 4\ell$ decays ($\ell = e, \mu$), recorded with the CMS detector in 2011 and 2012. The differential cross section measurements are performed in bins of the transverse momentum and rapidity of the four-lepton system, invariant masses of the two lepton pairs, five helicity angles formed by the leptons in the Collins-Soper frame, jet multiplicity, transverse momentum of the leading jet, and distance in rapidity between the Higgs boson candidate and the leading jet. The measurement of the cross section of the Z boson production in $Z \rightarrow 4\ell$ decay channel and its ratio to the Higgs boson production cross section in $H \rightarrow 4\ell$ channel is also performed. All results are corrected for the detection efficiency and resolution effects. The inclusive fiducial cross section for the Higgs boson production in $H \rightarrow 4\ell$ decay channel is measured to be $0.56^{\rm +0.67}_{\rm -0.44} \, {\rm(stat.)}\, ^{\rm +0.21}_{\rm -0.06}\, {\rm (sys.)}$~fb for proton collisions at 7~TeV and $1.11^{\rm +0.41}_{\rm -0.35} \, {\rm(stat.)}\, ^{\rm +0.14}_{\rm -0.10}\, {\rm (sys.)}$~fb for proton collisions at 8~TeV. The results of all measurements are compared with theoretical calculations based on Standard Model and no significant deviation is observed.