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

TL;DR

This paper reconstructs pion and kaon parton distribution functions (PDFs) from lattice QCD Mellin moments, revealing a $(1-x)^2$ behavior at large $x$ and analyzing SU(3) flavor symmetry breaking effects.

Contribution

It introduces a method to reconstruct $x$-dependent PDFs from lattice Mellin moments for pion and kaon, including higher moments up to $n=6$, and compares their flavor symmetry breaking effects.

Findings

Reconstructed PDFs favor a $(1-x)^2$ behavior at large $x$.

Higher moments $raket{x^n}$ for $4 extless n extless 6$ were extracted.

Comparison shows differences due to SU(3) flavor symmetry breaking.

Abstract

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