Observáveis em modelos efetivos confinantes: potencial quark–antiquark e momento magnético de núcleons

Abstract

The understanding of hadronic physics, in terms of quarks and gluons, is still an open problem, since the color confinement mechanism still lacks a satisfactory analytical description from first principles. However, in order to address confinement, some approaches have been developed that explore or even manage to access information from the low-energy region of Quantum Chromodynamics (QCD), i.e. the nonperturbative part of QCD, where it is considered that the explanation for confinement may lie. Among the different methods, we focus on those that arise from the nonperturbative consequences of Gribov copies, which modify the infrared behavior of Yang-Mills propagators, especially that of the gluon propagator. At the same time, these approaches are motivated by the nonperturbative first-principle numerical results of lattice QCD. In this thesis, we will study the following models: Gribov–Zwanziger (GZ), refined Gribov–Zwanziger (RGZ), and Curci-Ferrari (CF, or massive gluon model). In the case of the gluon propagator, the nonperturbative information present in these approaches generates a structure of complex poles, which violates the positivity reflection axiom related to the physical interpretation of a particle, which could be considered as an indication of gluon confinement. The search for other signs of confinement in these formalisms is obviously of great importance to establish their role as consistent infrared realizations of QCD. With this in mind, and assuming confinement as something intrinsic to QCD, in this thesis we investigate in some observables the consequences and phenomenological impact of the non-perturbative characteristics of the different approaches mentioned. First, related to the observable of the energy spectrum, we focus on the calculation and analysis of the static potential between a heavy quark–antiquark pair, whose linear behavior, corroborated by lattice QCD, is considered a sign of confinement. Our objective is also to verify the validity of the mentioned approaches and their compatibility with perturbative predictions, and also whether such models can produce quark confinement through a linear potential. Our results indicate that the calculated potentials are in agreement with the high-energy perturbative result and also that these potentials present interesting non-perturbative corrections. In the case of Curci-Ferrari (massive gluon), due to the systematic introduction of more interaction effects that include corrections at one and two loops, these become very significant due to the emergence of a semilinear behavior of its potential in the region of intermediate distances. The other observable studied in this thesis is the magnetic moment, in particular that of the proton. Due to the difficulty that the calculation presents, we adopted the constituent quark model (CQM), which within its own limitations allows us to calculate the magnetic moment of hadrons as a function of the magnetic moments of their constituent quarks. In order to extract the magnetic moment of the quarks and with the aim of studying the phenomenological impact of the different types of propagators of the GZ, RGZ, and CF approaches, we analyzed the quark-photon vertex (QPV) (up to the order of one it loop) focusing on the contribution coming from QCD, which depends on the gluon propagator. Our results indicate that the contributions of the different approaches to the magnetic moment of the quarks are smaller in relation to the perturbative result (massless gluon) since these are suppressed due to the mass terms present in the gluon propagators, which in the GZ and CF cases present a very similar behavior even if the GZ case has imaginary poles and the CF case does not (at tree level). In the RGZ case, due to the more elaborate structure and complex poles of its propagator, more contributions to the magnetic moment of the quarks appear, which may even exceed the value of the perturbative result for certain values of the RGZ parameters. Regarding the magnetic moment of the proton, calculated in CQM, the most interesting result arises when the mass of the constituent quark is adjusted to reproduce the mass of the proton. In this case, by adjusting the mass parameters of the mentioned approaches, we can reproduce the moment of the proton. The values obtained are even comparable to other mass values obtained for the gluon mass.