Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O espalhamento píon-núcleon é um processo de grande importância para o conhecimento das interações fortes por vários motivos. A existência de ressonâncias em colisões píon-núcleon é compatível com o modelo de quarks. A determinação do termo sigma dá acesso as propriedades do núcleon e a constante de acoplamento π-N é fundamental para os cálculos em física nuclear. Nesta dissertação usamos um método para implementar a condição de unitariedade elástica em uma amplitude de baixas energias que reproduz os comprimentos de espalhamento obtidos por Weinberg. A partir da amplitude corrigida em unitaridade que construimos, estudamos as propriedades de simetria de cruzamento da amplitude total e a violação de isospin. Em seguida mostramos que as sucessivas correções de unitariedade se tornam cada vez menores, concluindo que o método utilizado permite construir amplitudes parciais de espalhamento que corrigem a unitariedade elástica perturbativamente. / The pion-nucleon interaction is an important source of knowledge of the strong interaction.The properties of the baryon resonances produced in pion-nucleon collisions give strong support to the quark model. The amplitude is related to the value of the pion-nucleon sigmaterm which constrains models of nucleon structure. The pion-nucleon coupling constant provides fundamental input for the calculation of nuclear forces.In this thesis a method is used to implement the elastic unitarity condition for a low energy amplitude reproducing the Weinberg scattering lengths. We study the total amplitude crossing symmetry properties and the isospin violation from electromagnetic mass diference of the corrected amplitude. Finally we show that the next order unitarity corrections are small,allowing us to conclude that the proposed method is a consistent perturbative scheme to implement elastic unitarity constraint.

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. / Physics

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