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

TL;DR

This paper reports lattice QCD calculations of odd Mellin moments of the pion GPD up to fifth order, exploring skewness dependence and employing advanced renormalization and fitting techniques.

Contribution

It introduces a method to compute skewness-dependent moments of pion GPDs using lattice QCD with polynomiality constraints and resummed perturbative matching.

Findings

Results are consistent with previous lattice studies at zero skewness.

Skewness-dependent moments are obtained through polynomiality-constrained fits.

Calculations cover a range of momenta and momentum transfers.

Abstract

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution (GPD) up to fifth order, $\langle x^4\rangle$, 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.