Hadron Structure from lattice QCD in the context of the Electron-Ion Collider

Abstract

Hadron structure calculations using lattice Quantum Chromodynamics (QCD) have advanced significantly in recent years. Results for charges, form factors, and lower Mellin moments can be obtained to high precision, generalized parton distributions can now be computed either directly or reconstructed from moments, and transverse-momentum-dependent distributions can be accessed through direct lattice calculations. Together, these quantities provide detailed and complementary insights into the internal structure of hadrons. These theoretical developments are highly relevant to the experimental program of the Electron-Ion Collider (EIC) and of other facilities. We review the most pertinent lattice QCD results for hadron structure that inform the EIC scientific agenda, with particular emphasis on the pion, kaon, and nucleon.

Figures (21)

• Figure 1: Gauge ensembles used for hadron structure simulated for $m_\pi<145$ MeV.
• Figure 2: Pion vector form factor from: i) Left panel: ETMC results extrapolated to the chiral limit for low $Q^2$ compared to data from CERN ETM:2017wqc; ii) Middle panel: BNL/JLab results compared to experimental data and phenomenology Gao:2021xsm; iii) Right panel: $\chi$QCD for $m_\pi=252, 174$ and 137 MeV for intermediate $Q^2$Wang:2020nbf.
• Figure 3: LQCD results on the pion charge radius compared to the PDG value (gray band).
• Figure 4: Left: Continuum extrapolation of the momentum fraction of the pion and kaon using ETMC ensembles; Middle: Contributions of quarks and gluons to the pion and kaon momentum faction; Right: Comparison of the pion and kaon momentum fractions with other recent LQCD and phenomenology results. Figures are from Ref. ExtendedTwistedMass:2024kjf. The pion comparison figure includes the recent MIT group values Hackett:2023nkr.
• Figure 5: Results on the third and fourth unpolarized moments for the pion (left) and for the u-quark (middle) and s-quark (right) in the kaon. LQCD data are compared to analyses of experimental data and other theoretical determinations. The gray band denotes the spread of the values extracted from experimental data. All results are in the $\overline{\text{MS}}$ scheme at 2 GeV.