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Gluon and valence quark distributions for the pion and kaon in nuclear matter

In this paper we study the gluon and valence quark distributions in the pion and kaon in nuclear medium for various nuclear densities as well as in vacuum within the Nambu--Jona-Lasinio (NJL) model with the help of the proper-time regularization scheme which simulates a confinement of QCD. The nuclear medium effect is also determined in the same model for the symmetric nuclear matter. We then analyze the gluon and valence quark distributions for the bound pion and kaon in symmetric nuclear matter as well as those in vacuum. We find that the valence quark and gluon distributions in vacuum have relatively good agreements with the experimental data, the lattice QCD simulations, and the JAM Monte-Carlo (MC) global fit QCD analysis. Evolving to the higher factorization scale $Q = $ 4 GeV, the in-medium gluon and valence-quark distributions of the pion for various nuclear densities are turned out to be almost unchanged in comparison to the vacuum cases. On the contrary, for the kaon, they increase significantly with respect to the densities. Finally, we find that the vacuum gluon distribution for the kaon is smaller than that for the pion, which is consistent with other theoretical predictions. This feature holds for the in-medium gluon distribution in the nuclear density up to the saturation density.