Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

Abstract

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution (GPD) up to fifth order, $⟨x^4⟩$, and for the skewness range $[-0.33,0]$ using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing $a=0.04\mathrm{fm}$ and valence pion mass $300$ $\mathrm{MeV}$, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV${}^2$. We employ ratio-scheme renormalization and next-to-leading-logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

Comments: 22 pages, 15 figures