Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences


Physics and Astronomy

First Advisor

Dr. Keh-Fei Liu


Lattice Quantum Chromodynamics (QCD) provides a way to have a precise calculation and a new way of understanding the hadrons from first principles. From this perspective, this dissertation focuses first on a precise calculation of the pion form factor using overlap fermions on six ensembles of 2+1-flavor domain-wall configurations generated by the RBC/UKQCD collaboration with pion masses varying from 137 to 339 MeV. Taking advantage of the fast Fourier transform, low-mode substitution (LMS) and the multi-mass algorithm to access many combinations of source and sink momenta, we have done a simulation with various valence quark masses and with a range of space-like Q2 up to 1.0 GeV 2 . With a z-expansion fitting of our data, we find the pion mean square charge radius to be r2π = 0.433(9)(13) fm2, which agrees well with the experimental result, and includes the systematic uncertainties from chiral extrapolation, lattice spacing, and finite volume dependence. We also find that r2π depends on both the valence and sea quark masses strongly and predict the pion form factor up to Q2 = 1.0 GeV 2 which agrees with experiments very well. The second topic is the lattice calculation of proton momentum and angular momentum fractions. As confirmed from experiment and lattice QCD calculation, the total helicity contribution from quarks is about ~ 30% of the proton spin. Determination of the rest of the contributions from quarks and gluons to the proton spin is a challenging and important problem. On the lattice side, one way to approach this problem is to use the nucleon matrix element of the traceless, symmetric energy-momentum tensor (EMT) to determine the momentum and angular momentum distributions of up, down, strange and glue constituents. Since the EMT of each parton species are not separately conserved, we summarized their final angular momentum fractions by considering mixing and non-perturbative renormalization at MS(μ = 2 GeV) and use the momentum and angular momentum sum rules to normalize them. In order to have a complete picture of these quantities, we have calculated both the connected and disconnected insertions with an extrapolation to physical pion mass. We also use various techniques to improve the results, such as LMS and new three-point function contractions using fast Fourier transform for the connected insertions.

Digital Object Identifier (DOI)