| Popis: |
We present a calculation of the pion and kaon Mellin moment ⟨x3⟩ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark (Nf=2+1+1) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass ∼260 MeV, and a kaon mass ∼530 MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of 1.12–1.67 fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated nonperturbatively. Our results are converted to the MS¯ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are ⟨x3⟩πu+=0.024(18)stat(2)syst, ⟨x3⟩Ku+=0.035(6)stat(3)syst, and ⟨x3⟩Ks+=0.075(5)stat(1)syst, where the systematic error is the uncertainty due to excited state contamination. We combine ⟨x3⟩ with the two lower moments, namely ⟨x⟩ and ⟨x2⟩, to obtain the ratios ⟨x3⟩/⟨x⟩ and ⟨x3⟩/⟨x2⟩, as well as ⟨x3⟩Ku+/⟨x3⟩πu+ and ⟨x3⟩Ku+/⟨x3⟩πu+. In addition, we reconstruct the x-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large x-dependence that falls as (1−x)2 for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with 4≤n≤6. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking. |
