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We present a calculation of the connected-diagram contributions to the firstthree non-trivial Mellin moments for the pion and kaon, extracted using localoperators with up to 3 covariant derivatives. We use one ensemble of gaugeconfigurations with two degenerate light, a strange and a charm quark($N_f$=2+1+1) of maximally twisted mass fermions with clover improvement. Theensemble has a pion mass $\sim$260 MeV, and a kaon mass $\sim$530 MeV. Wereconstruct the $x$-dependence of the PDFs via fits to our results, and findthat our lattice data favor a $(1-x)^2$-behavior in the large-$x$ region forboth the pion and kaon PDFs. We integrate the reconstructed PDFs to extract thehigher moments, $\langle x^n \rangle$, with $4 \leq n \leq 6$. Finally, wecompare the pion and kaon PDFs, as well as the ratios of their Mellin moments,to address the effect of SU(3) flavor symmetry breaking.

$x$-dependence reconstruction of pion and kaon PDFs from Mellin moments