Hadron Structure

TL;DR

This review surveys recent Lattice QCD advances in hadron structure, emphasizing nucleon observables (g_A, EM form factors, Dirac/Pauli radii, momentum fraction, spin) near the physical pion mass, as well as hyperon and meson form factors. It details systematic uncertainties (excited-state contamination, finite volume, renormalization, and disconnected diagrams) and highlights methodological progress (All-Mode-Averaging, hierarchical probing, variational methods, Feynman-Hellmann). The work shows encouraging agreement with experimental benchmarks for several quantities at near-physical masses, while underscoring remaining challenges such as precise control of disconnected contributions and multi-particle resonances. The insights aim to guide ongoing efforts to extract reliable Standard-Model inputs and constrain beyond-Standard-Model scenarios from hadron structure.

Abstract

This is a review of recent developments in hadron structure within the framework of Lattice QCD. The main focus is on recent achievements in the evaluation of nucleon quantities, such as the axial charge, electromagnetic form factors, the Dirac and Pauli radii, the quark momentum fraction and the spin content of the nucleon, in view of simulations at pion masses very close to their physical value. A discussion of the systematic uncertainties and the computation of the disconnected contributions using dynamical simulations is also included. Results emerging the properties of particles other than the nucleon are summarized, highlighting selected hyperon and meson form factors.

Figures (19)

• Figure 1: Connected (left) and disconnected (right) contributions to the nucleon three-point function.
• Figure 2: Collection of lattice results for $g_A$. In chronological order these correspond to: $N_f{=}2{+}1$ DWF (RBC/UKQCD Yamazaki:2008pyYamazaki:2009zq, RBC/UKQCD Ohta:2013qda, $\chi$QCD chiQCD14), $N_f{=}2{+}1$ DWF on asqtad sea (LHPC Bratt:2010jn), $N_f{=}2$ TMF (ETMC Alexandrou:2010hf), $N_f{=}2$ Clover (QCDSF/UKQCD Pleiter:2011gw, CLS/MAINZ Capitani:2012gj, QCDSF Horsley:2013ayv, RQCD Bali:2013nlaRQCD14), $N_f{=}1{+}2$ Clover (LHPC Green:2012rr, CSSM Owen:2012ts), $N_f{=}2{+}1{+}1$ TMF (ETMC Alexandrou:2013joa), $N_f{=}2{+}1{+}1$ HISQ (PNDME Bhattacharya:2013ehcPNDME14), $N_f{=}2$ TMF with Clover (ETMC ETMC14). The asterisk is the experimental value.
• Figure 3: The axial charge as a function of the lattice spacing. The data correspond to: a. TM fermions (ETMC): open/filled symbols for $m_\pi\sim465\,/260$ MeV, b. HISQ fermions (PNDME): open/filled symbols for $m_\pi\sim310\,/220$ MeV, c. Clover fermions (RQCD): open/filled symbols for $m_\pi\sim420\,/280$ MeV. Points have been horizontally shifted for clarity.
• Figure 4: The axial charge as a function of the source-sink separation for (a). $N_f{=}2$ Clover fermions at $m_\pi~300$ MeV (RQCD RQCD14), and (b). $N_f{=}2{+}1{+}1$ TMF (ETMC Dinter:2011sg).
• Figure 5: (a). The ratio of the axial charge for $N_f{=}2{+}1{+}1$ TMF (ETMC Alexandrou:2013joa), (b). Bare values for $g_A$ as a function of the source-sink separation using $N_f{=}2{+}1{+}1$ HISQ fermions at $m_\pi=310$ MeV.