Higher Mellin Moments of the Unpolarized PDF of the Pion and the Kaon from Lattice QCD

We present results on the Mellin moments of the unpolarized parton distribution function (PDF) of the pion and kaon up to the fourth order. The computation is done using one $N_f=2+1+1$ gauge ensemble of twisted mass fermions with quark masses tuned to approximately their physical values. We reconstruct the valence pion and kaon PDFs using the connected contributions to the three Mellin moments. We compare our results on the Mellin moments and the reconstructed PDFs with other lattice QCD and phenomenological determinations.