Review of Hadron Structure Calculations on a Lattice

TL;DR

This review assesses the progress of lattice QCD in hadron structure, focusing on benchmark quantities, form factors, wave functions, and the proton spin decomposition. It highlights advances toward physical-point calculations and improved control of systematic effects, while illustrating that excited-state contamination and finite-volume/discretization uncertainties remain significant for several observables. Encouraging agreement with experiment is reported for certain quantities such as $g_A$, $\langle x \rangle_{u-d}$, and $\kappa^v$ at light pion masses, though others show pronounced sensitivity to $m_\pi$ and $Q^2$ requiring careful analysis. The proton spin discussion reveals a complex budget with both quark/gluon angular momentum and disconnected contributions playing roles, underscoring the need for fully dynamical, disconnected-including studies to complete the picture.

Abstract

I present a review of the current status and the most recent achievements in lattice QCD calculations of hadron structure. First, I overview the status and systematic uncertainties of nucleon structure "benchmark" quantities that are well known from experiments and serve as a reference point for the validity of lattice QCD methods. Next, I discuss the current status of calculations of form factors of the nucleon and highlight some recent results for other hadrons that are important for understanding their internal dynamics. Wave functions of hadrons and their excitations may also be studied in lattice QCD, and I illustrate it with two recent examples of such calculations. Finally, I discuss in detail the state of calculations pertaining to the nucleon spin puzzle.

Figures (15)

• Figure 1: nameref-fig:gA-summary fith LAB: fig:gA-summary Summary of nucleon axial charge $g_A$ lattice results Owen:2012tsAlexandrou:2010hfAlexandrou:2011aaAlexandrou:2013joaBhattacharya:2013ehcCapitani:2012gjQCDSF:2011aaHorsley:2013ayvOhta:2013qdaBratt:2010jnGreen:2012ud.
• Figure 2: nameref-fig:gA-vs-Ls-Lt fith LAB: fig:gA-vs-Ls-Lt Detailed study of $g_A$ dependence on volume and temperature with Wilson fermions, $m_\pi\approx250\text{ MeV}$Green:2013hja.
• Figure 3: nameref-fig:xv-summary fith LAB: fig:xv-summary Summary of quark momentum fraction $\langle x\rangle_{u-d}^{\overline{MS}(2\text{ GeV})}$ lattice results Alexandrou:2013joaAoki:2010xgBali:2012avPleiter:2011gwBratt:2010jnGreen:2012ud.
• Figure 4: nameref-fig:xv-exc-states fith LAB: fig:xv-exc-states Excited state contributions to bare $\langle x\rangle_{u-d}$ and their removal using the summation method Jager:2013kha.
• Figure 5: nameref-fig:r1v-summary fith LAB: fig:r1v-summary Summary of $(r_1^2)^v$ lattice results Collins:2011mkBhattacharya:2013ehcCapitani:2012efAlexandrou:2013joaLin:2013bxaSyritsyn:2009npBratt:2010jnGreen:2012ud.