##### Correlation Functions in Pure Gauge Theories: Propagators and Vertices in Lattice QCD

Authors: Anthony G. Duarte

Ref.: (2016)

Abstract: This dissertation is a result of the work developed throughout the year by the author in association with his supervisors. There were two main objectives: one was to study the gluon and ghost propagators and the strong coupling constant on the lattice, namely their dependences on the finite lattice spacing and on the physical volume; the other was to compute the three-gluon vertex and provide further evidence of the zero crossing of the gluon form factor associated with the three gluon one particle irreducible function, which is expected so that one has a properly defined set of Dyson-Schwinger equations. These were done in the pure Yang-Mills theory. Our results showed noticeable (or, at most, mild) dependence of the gluon and ghost propagators on the physical volume, at least for the lattices used (above $(6.5 fm)^4$ and below $(13 fm)^4$); they showed on both propagators a dependence on the lattice spacing in the infrared region, where the dependence is more noticeable in the case of the gluon propagator; they exhibit a suppression on the value at the maximum of the running coupling for smaller lattice spacings. In what concerns the three gluon vertex, our results are in favour of a zero crossing of the gluon form factor for momenta in the range $p \in [220-260]$ MeV. On the other hand, the data seems to corroborate the predictions of the renormalisation group improved perturbation theory in the region of high momentum. The results obtained originated * Two papers in international refereed journals 1- "Lattice Gluon and Ghost Propagators, and the Strong Coupling Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects", Anthony G. Duarte and Orlando Oliveira and Paulo J. Silva, Phys Rev D94, 014502 (2016); 2- "Further Evidence for Zero Crossing on the Three Gluon Vertex", Anthony G. Duarte and Orlando Oliveira and Paulo J. Silva, Phys. Rev. D (accepted). * An oral presentation in an international conference 1- "Landau gauge gluon vertices from Lattice QCD", A. Duarte, O. Oliveira, P. J. Silva, presented in "34th International Symposium on Lattice Field Theory", Southampton, UK, 24-30 July 2016 which is going to be published in the proceedings 1- "Landau gauge gluon vertices from Lattice QCD", A. Duarte, O. Oliveira, P. J. Silva, PoS (LATTICE2016) 351 (in preparation)