Measurement of Z+b jets cross section in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

The measurements of the cross section of the Z boson, decaying to dielectrons or dimuons, in association with at least one bottom quark jet are performed with proton-proton collision data at $\sqrt{s}=13~\mathrm{TeV}$. The data sample corresponds to an integrated luminosity of $137.1~\mathrm{fb}^{-1}$, collected by the CMS experiment at the LHC. The integrated cross sections of Z$~+\geq$ 1 b jet and Z$~+\geq$ 2 b jets are reported for the electron, muon, and combined channels with full Run 2 data. The measured integrated cross sections are 6.52 $\pm$ 0.04 (stat) $\pm$ 0.40 (syst) $\pm$ 0.14 (theo) pb for Z$~+\geq$ 1 b jet and 0.65 $\pm$ 0.03 (stat) $\pm$ 0.07 (syst) $\pm$ 0.02 (theo) pb for Z$~+\geq$ 2 b jets. The differential cross section distributions are measured as a function of various kinematic observables that are useful for precision tests of the perturbative quantum chromodynamics predictions. The ratios of integrated and differential cross sections of Z$~+\geq$ 2 b jets and Z$~+\geq$ 1 b jet processes are also determined. The value of the integrated cross section ratio measured in the combined channel is 0.100 $\pm$ 0.005 (stat) $\pm$ 0.007 (syst) $\pm$ 0.003 (theo). All of the measurements are compared with predictions from Monte Carlo simulations.