[Paper Review] Hadron Structure

Martha Constantinou|arXiv (Cornell University)|Nov 1, 2014

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This review presents recent advances in lattice QCD simulations for hadron structure, focusing on precise calculations of nucleon properties—such as the axial charge, electromagnetic form factors, and spin content—at pion masses near the physical value. It addresses systematic uncertainties and disconnected quark contractions, with results for nucleons, hyperons, and mesons highlighting improved accuracy in hadron spectroscopy and form factors.

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.

Motivation & Objective

• To review recent progress in lattice QCD for calculating nucleon properties with high precision.
• To address systematic uncertainties in lattice QFT simulations, particularly from disconnected quark contractions.
• To present results for nucleon quantities such as the axial charge, electromagnetic form factors, and spin content at physical pion masses.
• To extend the analysis to hyperons and mesons, summarizing their form factors and structural properties.
• To evaluate the impact of dynamical fermions and improved algorithms on the accuracy of hadron structure observables.

Proposed method

• Utilizes large-scale lattice QCD simulations with dynamical quarks to compute hadron matrix elements.
• Applies improved gauge and fermion actions to reduce discretization errors and reach pion masses close to the physical value.
• Employs stochastic estimation techniques to compute disconnected quark contractions, a major source of systematic uncertainty.
• Uses variational methods and multiple source/sink states to extract excited-state contributions and improve signal-to-noise ratios.
• Applies extrapolation techniques to physical point using chiral perturbation theory and continuum limit analysis.
• Computes matrix elements of local currents (e.g., vector, axial-vector, scalar) to extract form factors and radii.

Experimental results

Research questions

• RQ1 How accurately can lattice QCD compute the nucleon axial charge at physical pion mass?
• RQ2 What are the contributions of disconnected quark contractions to nucleon electromagnetic form factors?
• RQ3 How do the Dirac and Pauli radii of the nucleon compare with experimental data and theoretical expectations?
• RQ4 What is the quark momentum fraction and spin content of the nucleon as computed in lattice QCD?
• RQ5 What are the electromagnetic and weak form factors of hyperons and light mesons in modern dynamical simulations?

Key findings

• The nucleon axial charge is computed with high precision at physical pion masses, showing consistency with experimental values.
• Disconnected quark contractions are successfully evaluated using stochastic estimators, reducing systematic errors in form factor calculations.
• The Dirac and Pauli radii of the nucleon are determined with improved accuracy, showing good agreement with phenomenological fits.
• The quark momentum fraction and spin content of the nucleon are extracted with reduced uncertainties, supporting the dominance of valence quark contributions.
• Hyperon and meson form factors are computed with increasing precision, revealing non-trivial structure beyond the nucleon.
• Systematic uncertainties from chiral extrapolation and finite-volume effects are quantified and minimized through advanced simulation techniques.