Nucleon Parton Distribution Functions from Boosted Correlations in the Coulomb gauge

TL;DR

This paper explores a new Coulomb gauge lattice QCD method for calculating nucleon parton distribution functions, showing promising results for valence PDFs and highlighting challenges with excited-state contamination.

Contribution

First implementation of Coulomb gauge boosted correlators for nucleon PDFs, offering an alternative to Wilson line methods and demonstrating its potential effectiveness.

Findings

Valence PDFs agree with global analyses at high momentum

Discrepancies in full-quark PDFs due to excited-state contamination

Higher nucleon momentum results are more consistent with phenomenology

Abstract

Recently, a novel approach has been proposed to compute parton distributions through the use of boosted correlators fixed in the Coulomb gauge from lattice QCD, within the framework of Large-Momentum Effective Theory (LaMET). This approach circumvents the need for Wilson lines, potentially enhancing the efficiency and accuracy of lattice calculations. In this work, we present the first exploratory implementation of the Coulomb gauge method for calculating nucleon unpolarized, helicity, and transversity parton distribution functions (PDFs). The calculations are performed on a Highly-Improved-Staggered-Quark ensemble with lattice spacing $a = 0.06$ fm, volume $L_s^3 \times L_t=48^3\times 64$, and valence pion mass $m_\pi=300$ MeV, employing boosted nucleon states with momenta up to 3.04 GeV. Our lattice predictions for the valence-quark PDFs -- extracted from the real part of the correlators -- show good convergence with increasing nucleon momentum and are compatible with the most recent global analyses for all spin structures. On the other hand, the full-quark-channel PDFs obtained from the imaginary part of the correlators exhibit discrepancies between the two large nucleon momenta considered, although the results at the higher momentum are consistent with phenomenology. The discrepancies are likely driven by stronger excited-state contamination in the imaginary matrix elements, which is consistent with the observation in the literature. Overall, this work demonstrates the efficacy of the Coulomb gauge approach for nucleon PDFs and serves as a benchmark for its broader applications.