Nucleon structure with two flavors of dynamical domain-wall fermions

TL;DR

This paper reports a lattice QCD calculation of nucleon structure using dynamical domain-wall fermions, providing insights into form factors, moments of structure functions, and their agreement with experimental data.

Contribution

First lattice QCD study employing two flavors of dynamical domain-wall fermions to compute nucleon form factors and structure function moments with controlled chiral symmetry breaking.

Findings

The ratio g_A/g_V trends lower than experimental value at lighter quark masses.

Goldberger-Treiman relation holds at low momentum transfer, estimating g_{πNN} = 15.5(1.4).

Quark momentum and helicity fractions overshoot experimental values after chiral extrapolation.

Abstract

We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is about $(1.9{fm})^3$. The ratio of the isovector vector to axial charges, $g_A/g_V$, trends a bit lower than the experimental value as the quark mass is reduced toward the physical point. We calculate the momentum-transfer dependences of the isovector vector, axial, induced tensor and induced pseudoscalar form factors. The Goldberger-Treiman relation holds at low momentum transfer and yields a pion-nucleon coupling, $g_{\pi NN} = 15.5(1.4)$, where the quoted error is only statistical. We find that the flavor non-singlet quark momentum fraction $<x>_{u-d}$ and quark helicity fraction $<x>_{\Delta u-\Delta d}$ overshoot their experimental values after linear chiral extrapolation. We obtain the transversity, $<1 >_{\delta u-\delta d} = 0.93(6)$ in $\bar{\rm MS}$ at 2 GeV and a twist-3 polarized moment, $d_1$, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss the systematic errors in the calculation, with particular attention paid to finite-volume effects, excited-state contamination, and chiral extrapolations.