Hadron structure with light dynamical quarks

TL;DR

This work demonstrates that a hybrid lattice QCD approach with Asqtad sea quarks and domain-wall valence quarks can probe generalized parton distributions and related form factors of the nucleon at light quark masses, down to $m_\pi \approx 350$ MeV. By computing moments of parton distributions and the lowest generalized form factors, the study examines both forward and off-forward nucleon structure, including the energy-momentum tensor, while testing the nonperturbative renormalization patterns and finite-size effects. Key findings include isovector electromagnetic form factors displaying dipole-like behavior, evidence for non-factorization of $x$- and $t$-dependence in GPDs, and progress toward the physical axial coupling $g_A$, alongside ongoing challenges in $\langle x\rangle$ and tensor charges across lattice actions. The work also explores the feasibility of accessing higher $Q^2$ on the lattice, highlighting substantial statistical demands and the need for variance-reduction techniques to reach the perturbative QCD regime, with significant implications for connecting lattice results to experimental observables and chiral EFT predictions.

Abstract

Generalized parton distributions encompass a wealth of information concerning the three-dimensional quark and gluon structure of the nucleon, and thus provide an ideal focus for the study of hadron structure using lattice QCD. The special limits corresponding to form factors and parton distributions are well explored experimentally, providing clear tests of lattice calculations, and the lack of experimental data for more general cases provides opportunities for genuine predictions and for guiding experiment. We present results from hybrid calculations with improved staggered (Asqtad) sea quarks and domain wall valence quarks at pion masses down to 350 MeV.

Figures (12)

• Figure 1: $\langle 1\rangle_{\Delta u-\Delta d}$
• Figure 2: $\langle 1\rangle_{\delta u-\delta d}$
• Figure 3: $\langle x\rangle_{u-d}$
• Figure 4: $\langle x\rangle_{u-d}/\langle x\rangle_{\Delta u-\Delta d}$
• Figure 5: The electromagnetic form factors of the nucleon at small values of $Q^2$.