Nucleon structure with two flavors of dynamical domain-wall fermions

TL;DR

The paper advances nucleon structure calculations by performing a two-flavor dynamical lattice QCD study with domain-wall fermions, achieving good chiral symmetry and nonperturbative renormalization. It provides isovector form factors ($G_V$, $G_A$, $G_T$, $G_P$) and moments of structure functions ($\langle x\rangle_{u-d}$, $\langle x\rangle_{\Delta u-\Delta d}$, transversity, $d_1$), highlighting finite-volume and chiral extrapolation challenges. Key findings include a near-experimental $g_A/g_V$ only when excluding the lightest mass, smaller-than-expected Dirac and axial radii, a consistent though mass-dependent pion-nucleon coupling via the Goldberger–Treiman relation, and transversity around $0.93$ at 2 GeV, with twist-3 moment compatible with Wandzura–Wilczek. The work underscores significant finite-volume and chiral-systematics at current masses and motivates simulations at lighter pions and larger volumes to approach physical QCD behavior.

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, $g_{πNN} = 15.5(1.4)$, where the quoted error is only statistical. We find that the flavor non-singlet quark momentum fraction $<x>_{u-d}$ and quark helicity fraction $<x>_{Δu-Δd}$ overshoot their experimental values after linear chiral extrapolation. We obtain the transversity, $<1 >_{δu-δd} = 0.93(6)$ 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.

Figures (36)

• Figure 1: Renormalized isovector axial charge $g_{A}/g_{V}$ calculated with box Ohta:2004mg and Gaussian smeared sources with various source-sink separations ($t_{\rm sep}$). The value from the Gaussian source with $t_{\rm sep}=10$ and smearing radius 4.35 at the lightest quark mass of $m_f=0.02$ deviates significantly from the previous box-source calculation. In that case the box size is chosen for better overlap with the ground state of the nucleon and the longer source-sink separation ($t_{\rm sep}=12$) is adopted to avoid possible excited-state contaminations. This discrepancy is not resolved by using a Gaussian source of an radius 8 and the same source-sink separation. As discussed in the text, this is likely caused by the larger statistical fluctuation in the longer source-sink separation.
• Figure 2: Nucleon effective mass plots from two-point functions. Gaussian source with smearing radius, $r_{\rm gauss}=4.35$ (left), 8 (center), and box source (right) from the calculation in Ref. Ohta:2004mg.
• Figure 3: Comparison of the bare isovector vector charge $g_{V}$ (top) and axial charge $g_{A}$ (bottom) from source-sink separation $t_{\rm sep}=10$ Gaussian source (left panels), $t_{\rm sep}=12$ Gaussian source (middle panels) and $t_{\rm sep}=12$ box source (right panels).
• Figure 5: Bare vector charge as a function of the current insertion time. Results are averaged over all sources. The top figure depicts $t_{\rm sep}=12$ calculation at the lightest quark mass, $m_f=0.02$. The other three figures are obtained from $t_{\rm sep}=10$ calculations at all three quark masses (in order of increasing mass from top to bottom). The fit ranges are shown by horizontal lines.
• Figure 6: The isovector vector-charge $(g_V)^{\rm bare}$ as a function of the pion mass squared.