Aspects of universal extra dimensional models and their latticized versions.

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The first part of the thesis deals with models with universal dimensions, models in which all the Standard Model particles propagate in the extra dimension. These models have the interesting property that at low energies there are no tree-level effects of the extra dimensions. Therefore, as long as the new particles are heavy enough, the first effects of the extra dimensions will appear at one loop, and will be suppressed. As a consequence, new particles related with the extra dimensions can be relatively light ( or, equivalently, the extra dimensions relatively large ). It is therefore very important to determine how light those particles could be, and analyze if they can be produced at the present or immediate future experimental facilities. The thesis analyzes the one-loop contributions of one universal extra dimension to the decay of the Z in the b-quark anti-b channel , which displays strong dependences on the top-quark mass and is well determined from experiment. This process provides the best limit on the mass of the lightest new particle (together with the one obtained from the rho parameter). However, it is only about 300 GeV (95 \% CL) making the new particles accessible to experimental facilities such as the Large Hadron Collider. In the second part, the thesis studies the question of power corrections to gauge couplings in models with extra dimensions. This is a very important question because if those corrections could be controlled it might be possible to test Grand Unification models at energies accessible at experiment. The question is also involved because the non-renormalizability of gauge theories in more than four dimensions. Using a full continuum effective field theory approach, based on dimensional regularization, the thesis concludes that power corrections can be computed reliably only if the more complete theory that generates them is known. Finally the thesis presents the latticized versions of two models with extra dimensions (universal extra dimension and with only Higgs and gauge bosons propagating in the extra dimension) and studies their relevant phenomenology. The topics studied in this thesis require a good knowledge of the language and techniques of the effective field theories as well as the calculational abilities to compute electroweak corrections. In addition thorough understanding of the theoretical structure of the standard model is needed, as well as the phenomenological details of the top and b-quark physics. ____________________________________________________________________________________________________ RESUMEN La primera parte de la tesis está relacionada con modelos con dimensiones extra universales (todas las partículas se propagan en la dimensión extra). En estos modelos, a bajas energías, los primeros efectos aparecen al nivel de un loop. Como consecuencia, nuevas partículas relacionadas con las dimensiones extra pueden ser relativamente ligeras. En esta parte se analiza quan ligeras pueden ser y si pueden ser producidas en las actuales o inmediatamente futuras instalaciones experimentales. La tesis estudia las contribuciones a la desintegración del Z en quarks b, la cual muestra una fuerte dependencia con la masa del top y experimentalmente está bien medida . Este proceso proporciona el mejor límite en la masa de las nuevas partículas, junto con el obtenido del parámetro rho. De todos modos, solo es 300 GeV (95 % CL), lo que hace accesibles las nuevas partículas a las futuras instalaciones experimentales. En la segunda parte, se estudian las correcciones a las constantes gauge en forma de potencias en modelos con dimensiones extra. Lo cual es muy importante porque si estas correcciones pudiesen ser controladas podría ser posible comprobar modelos de Gran Unificación a bajas energías. Usando teorías efectivas, se concluye en la tesis que estas correcciones pueden ser calculadas sin ambigüedad solo cuando se conoce, aunque sea parcialmente, la teoría más completa que genera la teoría extra dimensional. Finalmente la tesis presenta las versiones latizadas de dos modelos diferentes con dimensiones extra y estudia su fenomenología.
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