• Hadron Structure From Lattice Quantum Chromodynamics Using Twisted Mass Fermions

      Constantinou, Martha; Metz, Andreas; Sparveris, Nikolaos; Cichy, Krzysztof (Temple University. Libraries, 2021)
      Hadron structure is an important field in particle physics because hadrons make up most of the matter in nature. The theory of the strong nuclear force, via which the partons of hadrons interact, is Quantum Chromodynamics (QCD) and cannot be solved analytically. Lattice QCD (LQCD) is an ideal formulation of QCD and is the only formulation starting from first principles. In this thesis, we use LQCD for two primary topics of study: 1) nucleon structure and 2) pion and kaon structure. In the first study, we calculate the quark momentum fraction, helicity, and transversity for the nucleon. The calculations are performed on three ensembles at the physical point of the pion mass allowing us to study finite volume, discretization, strange and charm quark quenching, and excited-state systematic effects. Our calculations of the helicity and transversity are first predictions at the physical point. In the second study, we investigate pion and kaon structure. We calculate the first three non-trivial Mellin moments of the meson parton distribution functions (PDFs). For the kaon, this is the first direct calculation of the second and third moments. We carefully choose which matrix elements we implement so that there is no mixing with lower derivative operators, avoiding systematic uncertainties which are not well understood. We also perform an extensive study of the excited-state contamination. In a pioneering study, we show that the full x-dependence of the PDFs can be calculated from the first three Mellin moments. Such a calculation was previously thought to be unfeasible using moments calculated from LQCD. Our reconstruction of the PDFs allow us to comment on SU(3) flavor symmetry breaking and the high-x behavior of the pion PDF which are both interesting topics in hadron structure.