Precision physics in Hadronic Tau Decays

In the Standard Model of Particle Physics, which gives a very precise description of nature at many different scales, hadronic tau decays occur through the interaction of two weak charged currents mediated by the W boson, so it becomes a very nice test of electroweak interactions. On the other hand, the quark current is responsible for a hadronic continuum, which allows to study strong interactions in the nonperturbative regime. In this thesis, some of the most powerful methods, such as the Operator Product Expansion (OPE) in the vacuum, effective field theories, dispersion relations or chiral perturbation theory have used for different phenomenological applications. The first application is the study of the extraction of physical parameters from the V-A spectral function. Using data provided by the ALEPH collaboration, we have obtained some LECs from Chiral Perturbation Theory and information on vacuum condensates. The V+A spectral function allows one of the most precise determination of the strong coupling. We have made a comprehensive analysis using ALEPH data, critically reviewing the strategies used in previous works and putting forward various approaches which allow to study complementary aspects of the problem. Our final result is in agreement with the PDG value. In the chiral limit, one can relate vacuum condensates to the electroweak penguin contribution of K → $\pi$$\pi$ processes, key for a better understanding of CP violation in kaons. We use those relations to find an updated value for the Q8 matrix element using the updated ALEPH V-A spectral function. Alternatively, we use those relations in the opposite direction to get an inclusive determination of the pion decay constant and an updated value for a D=8 condensate. Finally, we study the sensitivity of hadronic tau decays to physics beyond the Standard Model in the electroweak sector in the model independent framework of the Standard Model as Effective Field Theory. When integrating out the heavy particles of the SM, one have at first order in New Physics 5 new couplings for the nonstrange sector. Combining information from exclusive and inclusive observables, we are able to set competitive bounds for all of them. We compare with information that can be obtained from other Electroweak Precision Observables and LHC ones. We also make an exploratory study of the non-strange sector.