Moments of Nucleon Light Cone Quark Distributions Calculated in Full Lattice QCD

TL;DR

This work presents the first lattice QCD calculation of moments of nucleon light-cone quark distributions in full QCD, using Wilson fermions on 16^3×32 lattices with dynamical quarks. Moments are extracted via twist-2 operator matrix elements through the operator product expansion, with careful attention to operator construction, renormalization, and excited-state contamination. A key finding is that, at accessible quark masses, quenched and full QCD results agree within errors, suggesting small Dirac sea effects for these observables, while linear chiral extrapolation overestimates experimental values. Incorporating leading nonanalytic chiral behavior with a phenomenological cutoff reconciles several moments with experiment, and cooled (instanton-dominated) configurations corroborate the role of instantons and zero modes in nucleon structure.

Abstract

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $β= 5.6$ using configurations from the SESAM collaboration and at $β= 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.

Figures (26)

• Figure 1: Connected (upper row) and disconnected (lower row) diagrams contributing to hadron matrix elements. The left column shows typical contributions of quarks and the right column shows contributions of antiquarks.
• Figure 2: The rms radius of a gauge invariant smeared quark source as a function of the coefficient $\alpha$ and number of smearing steps $N$ defined in Eq. \ref{['opt-psi1Hpsi']}.
• Figure 3: Bootstrap distributions of $\langle x \rangle _q^{(b)}$ for ensembles of 25 (left plot) and 204 (right plot) SESAM configurations at $\kappa=0.1575$
• Figure 4: The scaled pion mass squared, $(a m_\pi)^2 \times (a_{5.6}/a)^2$, for the dynamical Wilson fermion calculations tabulated in Table \ref{['t_world-dyn-wil']}. The dotted line shows the mass at which the pion Compton wavelength equals one-fourth of the spatial dimension.
• Figure 5: Overlap between a smeared source and the proton ground state as a function of the source rms radius. The overlap for zero smearing is $6 \times10^{-5}$.