Aspects of quark and gluon structure of the proton, pion, and kaon from lattice quantum chromodynamics

Understanding the internal structure of hadrons from first principles is a central goal of modern nuclear and particle physics. Quantum Chromodynamics (QCD), the theory describing the strong interaction, governs the emergent properties of hadrons through the dynamics of quarks and gluons. In the non-perturbative regime, these interactions give rise to confinement, chiral symmetry breaking, and the emergence of hadron masses. In this thesis, we utilize lattice QCD, a discretized formulation of QCD in Euclidean spacetime, to perform calculations of physical quantities related to hadron structure. The lattice provides a systematically improvable framework for studying these quantities from first principles. This dissertation presents a study of several aspects of hadron structure using lattice QCD, with an emphasis on the pion, kaon, and proton. For the pion and kaon, we calculate the scalar, vector, and tensor form factors using ensembles of Nf = 2+1+1 twisted-mass clover-improved fermions and Iwasaki gauge action. These results provide quantitative insight into the electromagnetic and scalar radii, tensor anomalous magnetic moments, and the degree of SU(3) flavor-symmetry breaking. We further extend these studies to the generalized form factors and Mellin moments of the pion and kaon, establishing the hierarchy of moments and gaining insight into the three-dimensional structure of these mesons. For the proton, we present a continuum-limit extraction of the unpolarized gluon parton distribution function (PDF) using four different lattice spacings. This work employs the pseudo-distribution approach and systematically studies the effects of source–sink separation, smearing, and lattice spacing. We reconstruct the gluon PDF from coordinate-space matrix elements, quantify the impact of operator mixing with the quark singlet, and benchmark our results against phenomenological global analyses. In addition, we extract higher Mellin moments of the gluon PDF, focusing on the ratio ⟨x3⟩g/⟨x⟩g, and study their renormalization-group behavior. Together, these results advance our understanding of both the quark and gluon structure of hadrons, demonstrating the capabilities of lattice QCD as a precision tool for hadron structure. The synergy between lattice calculations, phenomenology, and forthcoming experimental programs such as the Electron-Ion Collider highlights the crucial role of first-principles theory in mapping the three-dimensional structure of matter.