Constraining gluon density of pions at large $x$ by pion-induced $J/\psi$ production

The gluon distributions of the pion obtained from various global fits exhibit large variations among them. Within the framework of the color evaporation model, we show that the existing pion-induced $J/\psi$ production data, usually not included in the global fits, can impose useful additional constraints on the pion parton distribution functions (PDFs). In particular, these data can probe the pion's gluon densities at large $x$. Existing pion-induced $J/\psi$ data covering a broad range of beam momenta are compared with next-to-leading-order QCD calculations using various sets of pion PDFs. It is found that $J/\psi$ data measured at forward rapidity and at sufficiently high beam momentum are sensitive to the large-$x$ gluon distribution of pions. The current $J/\psi$ data favor the Sutton-Martin-Roberts-Stirling and Gluck-Reya-Vogt pion PDFs, containing significant gluon content at large $x$.