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The baryon axial current in large $N_c$ chiral perturbation theory

In this thesis we calculate the baryon axial current within the combined framework of the $1/N_c$ expansion and chiral perturbation theory, where $N_c$ is the number of colors. This calculation shall consider Feynman diagrams to order of one-loop, octet and decuplet intermediaries states. We obtain corrections due to one-loop and perturbative SU(3) symmetry breaking. The first corrections come from Feynman diagrams, then talk about a broken chiral symmetry in the implicit limit $m_q \rightarrow 0$, where $m_q$ is the quark mass and the second corrections are obtained by ignoring isospin breaking and in that case the SU(3) symmetry breaking a first-order perturbation is included, leading an explicit break symmetry. The matrix elements of the spatial components of the axial operator between the states of the spin flavor symmetry, give the typical values of the axial vector coupling. For the baryon octet, links axial vector are $g_A$, just as they are defined in experiments of baryon semileptonic decays, where $g_A \approx 1.27$ for neutron beta decay. In strong decays of the baryon axial vector couplings are $g$, which are extracted from the widths of the strong decays of baryon decuplet to octet of baryons and pions. The calculation of this work allows us to make various settings by minimum squares, i.e., adjusting our analytical expressions with data pilot can make the comparison between theory and experiment. We found the comparison of our theoretical results with the experiment are in total agreement.