The fraction of $Z+$jet events that contain a charm jet is measured for the first time in the forward region of proton-proton collisions. The data sample used corresponds to an integrated luminosity of 6 fb$^{-1}$ collected at a center-of-mass energy of $13$ TeV with the LHCb detector. The ratio of production cross sections ${sigma(Zc)/sigma(Zj)}$ is determined in intervals of $Z$-boson rapidity in the range $2.0 < y(Z) < 4.5$. A sizable enhancement is observed in the forward-most $y(Z)$ interval, which could be indicative of a valence-like intrinsic-charm component in the proton wave function.
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