New dynamics in axions and flavor

Despite the great success of the Standard Model of Particle Physics in describing Nature, it
cannot account for some crucial experimental observations and theoretical issues. Therefore,
the Standard Model requires to be extended. This thesis is devoted to the study of two of the
theoretical issues: the absence of CP violation in the strong interactions, e.g. the strong CP
problem, and the tantalizing pattern of masses and mixings of the elementary fermions, that
is, the flavor puzzle. For both problems, novel (ultraviolet complete) dynamical solutions are
proposed. Complementarily, the model-independent techniques of effective field theories are
applied to chart new territory in the parameter space of axions and axion-like particles.

In the flavor arena, the leptonic flavor symmetry of the Standard Model is gauged, promoting
the Yukawa couplings to dynamical fields. The results of this theory are compared with those
expected from the effective ansatz of minimal flavour violation.
In the strong CP arena, two composite (dynamical) axion solutions to the strong CP problem
are proposed: in a first work the axion mass is raised in a framework with an unified strong
sector, while in a second work an invisible axion with an accidental Peccei-Quinn symmetry is
constructed.
In addition, new regions in parameter space for the effective couplings of axions and axion-
like particles are explored. In particular, this thesis goes beyond the one-coupling-at-a-time
approach, considering the simultaneous effect of several effective couplings: the axion coupling
to electroweak gauge bosons and the gluonic coupling in the first work, and the full bosonic
electroweak basis for a generic axion-like particle without gluonic coupling in the second one.