Measurement of differential cross sections for Z bosons produced in association with charm jets in pp collisions at $\sqrt{s}=$ 13 TeV

Measurements are presented of differential cross sections for the production of Z bosons in association with at least one jet initiated by a charm quark in pp collisions at $\sqrt{s}=$ 13 TeV. The data recorded by the CMS experiment at the LHC correspond to an integrated luminosity of 35.9 fb$^{-1}$. The final states that contain a pair of electrons or muons that are the decay products of a Z boson, and a jet consistent with being initiated by a charm quark produced in the hard interaction. Differential cross sections as a function of the $p_\mathrm{T}$ of the Z boson and $p_\mathrm{T}$ of the charm jet are compared with predictions from Monte Carlo event generators. The inclusive production cross section 405.4 $\pm$ 5.6 (stat) $\pm$ 24.3 (exp) $\pm$ 3.7 (thy) pb, is measured in a fiducial region requiring both leptons to have $\vert\eta\vert\lt$ 2.4 and $p_\mathrm{T}\gt10$ GeV, at least one lepton with $p_\mathrm{T}\gt$ 26 GeV, and a mass of the pair in the range 71-111 GeV, while the charm jet is required to have $p_\mathrm{T} \gt $ 30 GeV and $\vert\eta\vert\lt$ 2.4. These are the first measurements of these cross sections in proton-proton collisions at 13 TeV.