Reconstructing PDFs from Mellin moments: the pion and kaon case
Quantum Chromodynamics (QCD) is characterized by several emergent phenomena not apparent in the QCD Lagrangian, such as the dynamical chiral symmetry breaking (DCSB). In QCD, DCSB leads to an octet of Nambu-Goldstone bosons, which includes the triplet of pions and the four kaons. Kaons are particularly interesting because of the valence strange quark, which has a much larger mass than the up and down quarks that form the pions. Due to the presence of a valence strange quark in the kaon, a comparison between pion and kaon observables provides a unique window into the interplay between QCD dynamics and quark mass effects. Significant SU(3) flavor breaking effects have already been observed in the pion and kaon. Therefore, the study of quark contributions to the parton distribution functions is important for the qualitative understanding of these features.
While the proton has been extensively studied in lattice QCD, there are only limited pion and kaon structure studies. Given the relatively small number of experimental data, it is crucial to obtain results from first principles. In this talk, we present a direct lattice QCD calculation of the pion and kaon Mellin moments <x^2> with n<4. We use one ensemble of Nf=2+1+1 gauge configurations of maximally twisted mass fermions improved with a clover term. The ensemble corresponds to a pion mass of about 260 MeV and a kaon mass of about 530 MeV. We study excited-states contamination in detail using several values of the source-sink time separation within the range of 1.12 - 2.23fm. We use operators that are free of mixing and apply a multiplicative renormalization function calculated non-perturbatively. For <x>, we explore both the rest and boosted frame to draw conclusions on the excited states.
The most notable aspect is the reconstruction of the x-dependence of the pion and kaon PDFs using the Mellin moments calculated in this work. We find that the reconstruction is feasible, and we draw qualitative conclusions on the large-x behavior. The PDF reconstruction also allows the extraction of higher moments with reasonable statistical errors. 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.
Zoom link will be available via announcement email, or by contacting: ikolbe[at]uw.edu