Probing higher moments of pion parton distribution functions

TL;DR

This paper introduces a novel lattice QCD method using gradient flow to accurately determine higher moments of pion PDFs, overcoming previous divergence issues and achieving higher precision than traditional approaches.

Contribution

It demonstrates the first numerical application of gradient flow to extract higher moments of pion PDFs from lattice QCD, avoiding power divergent mixing.

Findings

Higher precision in moments compared to canonical methods

Successful extraction of ratios of moments from three-point functions

Potential to reach higher moments beyond previous limits

Abstract

We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower dimensional operators. We apply this method to obtain moments of the isovector PDF of the pion using four Stabilized Wilson Fermion ensembles with $m_{\pi}\simeq 411$ MeV and lattice spacings $a \simeq 0.064, 0.077, 0.094$, and $0.12$ fm. We present preliminary results of ratios of three-point functions as a function of flow time, which can be used to extract the ratios $\left\langle x^2 \right\rangle/\left\langle x \right\rangle$ and $\left\langle x^3 \right\rangle/\left\langle x \right\rangle$. We find that a significantly higher precision can be achieved with this method compared to the canonical approach, which requires boosting and cannot reach higher than the $\left\langle x^3 \right\rangle$ moment.