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In this paper we study the gluon and valence quark distributions in the pionand kaon in nuclear medium for various nuclear densities as well as in vacuumwithin the Nambu--Jona-Lasinio (NJL) model with the help of the proper-timeregularization scheme which simulates a confinement of QCD. The nuclear mediumeffect is also determined in the same model for the symmetric nuclear matter.We then analyze the gluon and valence quark distributions for the bound pionand kaon in symmetric nuclear matter as well as those in vacuum. We find thatthe valence quark and gluon distributions in vacuum have relatively goodagreements with the experimental data, the lattice QCD simulations, and the JAMMonte-Carlo (MC) global fit QCD analysis. Evolving to the higher factorizationscale $Q = $ 4 GeV, the in-medium gluon and valence-quark distributions of thepion for various nuclear densities are turned out to be almost unchanged incomparison to the vacuum cases. On the contrary, for the kaon, they increasesignificantly with respect to the densities. Finally, we find that the vacuumgluon distribution for the kaon is smaller than that for the pion, which isconsistent with other theoretical predictions. This feature holds for thein-medium gluon distribution in the nuclear density up to the saturationdensity.

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