Nucleon and pion gluon parton distribution function from lattice QCD calculation Fan, Zhouyou Physics Hadrons--Structure Gluons--Structure Partons Particles (Nuclear physics) Thesis Ph. D. Michigan State University. Physics 2022. Parton distribution functions (PDFs) are important to characterize the structure of the hadrons such as protons and neutrons. The contribution to the structure from quarks has been studied in detail during the past few decades. The structure in the gluon sector is also important but less studied. For high-energy hadrons, the gluon contribution dominates at small x, where x is the momentum fraction carried by a quark or gluon. At large x, the uncertainty of the gluon PDF is large, especially compared to that of the quark PDFs at large x. Gluon PDFs for nucleons and pions are mostly extracted from global analysis of experimental data using perturbation theory as a guide. Theoretically, lattice QCD provides an independent non-perturbative theoretical approach to calculate the gluon PDFs. We present the exploratory study of nucleon gluon PDFs from lattice QCD using the quasi-PDF approach. Using valence overlap fermions on the 2 + 1-flavor domain-wall fermion gauge ensemble, the quasi-PDF matrix elements we obtain agree with the Fourier transform of the global-fit PDF within statistical uncertainty. We further study the x-dependent nucleon and pion gluon distributions via the pseudo-PDF approach on lattice ensembles with 2 + 1 + 1 flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration. Using clover fermions for the valence action, and adding momentum smearing, PDFs are found for pion boost momenta up to 2.56 ⁹́⁸ GeV. Several lattice sizes and spacings (a ⁹́⁸ 0.9, 0.12 and 0.15 ⁹́⁸ fm) were evaluated, resulting in three pion masses, MÏ⁰ ⁹́⁸ 220, 310 and 690 ⁹́⁸ MeV/c2. Online resource; title from PDF title page (viewed on Oct. 12, 2023) Electronic resource. Includes bibliographical references (pages 113-131). Lin, Huey-Wen Yuan, Chien-Peng Pratt, Scott Huston, Joey Bazavov, Alexei 2022 text application/pdf 1 online resource (xv, 131 pages) : illustrations isbn:9798841787105 umi:29212490 local:Fan_grad.msu_0128D_19140 en In Copyright Ph. D. Doctoral Physics - Doctor of Philosophy Michigan State University