Far-forward production of charm mesons and neutrinos at Forward Physics Facilities at the LHC and the intrinsic charm in the proton

We discuss production of far-forward $D$ mesons/antimesons and neutrinos/antineutrinos from their semileptonic decays in pp-collisions at the LHC. We include the gluon-gluon fusion $gg \to c\bar{c}$, the intrinsic charm (IC) $gc \to gc$ as well as the recombination $gq \to Dc$ partonic mechanisms. The calculations are performed within the $k_T$-factorization approach and the hybrid model using different unintegrated parton distribution functions (uPDFs) for gluons from the literature, as well as within the collinear approach. We compare our results to the LHCb data for forward $D^{0}$-meson production at $\sqrt{s} = 13$ TeV for different rapidity bins in the interval $2 < y < 4.5$. The IC and recombination models are negligible at the LHCb kinematics. Both the mechanisms start to be crucial at larger rapidities and dominate over the standard charm production mechanisms. At high energies there are so far no experiments probing this region. We present also energy distributions for forward electron, muon and tau neutrinos to be measured at the LHC by the currently operating FASER$\nu$ experiment, as well as by future experiments like FASER$\nu2$ or FLArE, proposed very recently by the Forward Physics Facility project. Again components of different mechanisms are shown separately. For all kinds of neutrinos (electron, muon, tau) the subleading contributions, i.e. the IC and/or the recombination, dominate over light meson (pion, kaon) and the standard charm production contribution driven by fusion of gluons for neutrino energies $E_{\nu} \gtrsim 300$ GeV. For electron and muon neutrinos both the mechanisms lead to a similar production rates and their separation seems rather impossible. On the other hand, for $\nu_{\tau} + {\bar \nu}_{\tau}$ neutrino flux the recombination is further reduced making the measurement of the IC contribution very attractive.