Spin zero windows to new physics

This thesis pays special attention to fine-tunings of the SM, such as those characterising the strong CP problem and the electroweak hierarchy problem. Small parameters may be explained by approximate symmetries, serving as guideposts of symmetries yet undiscovered. Motivated by the use of hidden (or spontaneously broken) symmetries to explain the small parameters, which predict the existence of (pseudo)-Goldstone bosons, this thesis is structured around solutions to some of the problems of the SM which happen to require extra scalars and/or pseudoscalars.

In a first step, a theoretical proposal deals with the strong CP problem and the EW hierarchy problem simultaneously, studying the minimal extension of Goldstone Boson Higgs models which allows to implement the axion solution to the strong CP problem. In a second, more phenomenological step, the search for GBs in general will be tackled, using and developing the tool of effective Lagrangians to identify novel experimental proposals in the search for axions and axion-like particles at colliders. A third step of the exploration of the spin zero sector will concentrate on the case of scalar dark matter, reconsidering the phenomenological status of the Higgs portal scenario in the light of a more general formulation of effective field theories, and of new LHC signatures