Effective field theories for heavy and light fermions.

In this thesis, various aspects of different effective field theory (EFT) approximations to the Standard Model of elementary particle physics have been elaborated. The EFTs treated range from non-relativistic approximations to quantum electrodynamics (QED) and quantum chromodynamics (QCD), which can be applied if the quanta under consideration moves at velocities small compared with the speed of light, to chiral perturbation theory as well as the effective theory which emerges in the limit of a large number of colour degrees of freedom in QCD. The latter two constitute expansions in the energy of the process under investigation, and are applicable if this energy is small compared to a typical hadronic scale like, for example, the mass of the -meson. The first type of EFTs, namely NRQED and NRQCD, has been applied in chapter 2 and 3 to study the production cross section of tau lepton pairs as well as quark-antiquark pairs in electron-positron annihilation close to the production threshold, where the system is non-relativistic. In chapter 2 previous computations on tau threshold production are extended to the next-to-next-to-leading order in the velocity expansion and the full analytic form of the two-photon box amplitude, which had not been known explicitly before, is given. As an aside, in chapter 3 we discuss contributions to the total cross section of production of a heavy quark-antiquark pair which arise from intermediate states composed of light QCD degrees of freedom like light mesons or gluonia. These novel contributions constitute an advancement in the field of QCD sum rules for heavy quarks, since they point to the crucial necessity to exactly specify what is actually measured when one speaks about heavy quark production out of e+e- collisions. The second part of the thesis, chapters 4 and 5, tackles with several issues of low-energy hadronic physics. The effective approximation of QCD, chiral perturbation theory, as initially pioneered by Gasser and Leutwyler is only applicable up to energies roughly equal to the -meson mass. However, in recent years it proofed possible to extend this energy range by explicitly including higher resonance states into the effective Lagrangian. This so-called resonance chiral effective theory has been extended in chapter 3 to include a minimal odd-intrinsic parity sector constructed in such a way that it is fully compatible with short-distance QCD constraints. This is an important result for incorporating resonance fields in a chiral framework, and corrects a claim to the contrary put forward recently by other authors. As a by-product, predictions for odd-intrinsic-parity radiative decays of vector mesons in very good agreement with experiment are obtained. In the last chapter of this thesis, we move to the more crowded 1-2 Gev region in electron-positron annihilation where many more resonances need to be included in the field theoretic description. We outline the general strategy to follow in order to obtain a QCD-based parameterization of the total hadronic cross section at these energies, mainly focusing in the technical part of the analysis. A closed formula for the QCD vector-vector current correlator is proposed including contributions from resonance chiral theory at 1-loop with the odd-intrinsic-parity sector introduced before and resummation techniques. Although the practical implementation of the results shall require further investigations, this study shows that the use of EFTs of QCD in the intermediate energy region, populated by resonances, provides a powerful tool to endow the basic information of the underlying theory into the hadron phenomenology in an essentially model-independent way. __________________________________________________________________________________________________ RESUMEN Bajo el título de Effective field theories for heavy and light fermions se han englobado diversos temas relacionados con la aplicación de las teorías efectivas derivadas de la Electrodinámica y la Cromodinámica Cuántica a la producción de leptones y quarks a partir de la aniquilación de un par electrón-positrón. En el primer bloque, que se ocupa de la creación de sabores pesados, se estudia el cálculo de la sección eficaz de producción de leptones tau en la región umbral, y se hace una revisión profunda de la técnica de las reglas de suma para quarks pesados. La producción electromagnética de hadrones formados por quark ligeros se aborda en la segunda parte de esta tesis. En primer lugar se presenta el procedimiento para inferir relaciones entre las constantes del Lagrangiano efectivo con resonancias y QCD para el sector de paridad-intrínseca negativa, y a continuación se deriva una expresión teórica para el correlador de dos corrientes vectoriales en la región de las resonancias, cuya parte imaginaria se relaciona con la sección eficaz hadrónica