Measurement of the associated production of a Z boson with charm or bottom quark jets in proton-proton collisions at $\sqrt{s}=$ 13 TeV

Ratios of cross sections, $\sigma$(Z+c jets)/$\sigma$(Z+jets), $\sigma$(Z+b jets)/$\sigma$(Z+jets), and $\sigma$(Z+c jets)/$\sigma$(Z+b jets) in the associated production of a Z boson with at least one charm or bottom quark jet are measured in proton-proton collisions at $\sqrt{s}=$ 13 TeV. The data sample, collected by the CMS experiment at the CERN LHC, corresponds to an integrated luminosity of 35.9 fb${}^{-1}$, with a fiducial volume of $p_T>$ 30 GeV and $\eta <$ 2.4 for the jets, where $p_T$ and $\eta$ represent transverse momentum and pseudorapidity, respectively. The Z boson candidates come from leptonic decays into electrons or muons with $p_T>$ 25 GeV and $\eta <$ 2.4, and the dilepton mass satisfies 71 $<m_Z<$ 111 GeV. The measured values are $\sigma$(Z+c jets)/$\sigma$(Z+jets) = 0.102 $\pm$ 0.002 $\pm$ 0.009, $\sigma$(Z+b jets)/$\sigma$(Z+jets) = 0.0633 $\pm$ 0.0004 $\pm$ 0.0015, and $\sigma$(Z+c jets)/$\sigma$(Z+b jets) = 1.62 $\pm$ 0.03 $\pm$ 0.15. Results on the inclusive and differential cross section ratios as functions of jet and Z boson transverse momentum are compared with predictions from leading and next-to-leading order perturbative quantum chromodynamics calculations. These are the first measurements of the cross section ratios at 13 TeV, and the measurement precision is better than that of the current theoretical predictions.