Phenomenological Applications of Effective Field Theory: Neutrinos and LHC Physics

The understanding of the principles underlying the structure of fermion masses and mixing is one of the important open problems in present day research in particle physics. One way to address this problem is by means of a symmetry principle, as it has been often the case in particle physics. Several efforts have been spent in particular to understand lepton masses and mixing by means of flavour symmetries. The first part of this thesis deals with the following problem: can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing in the symmetric limit? Even though many models are available relying on specific flavour groups, a comprehensive analysis along the above direction is missing. We provide a complete answer to this question in two different cases of neutrino mass generation, from the Weinberg operator or from the seesaw mechanism. We allow the symmetry group to be as general as possible. We show that the pattern of lepton masses and mixing only depends on the dimension, type (real, pseudoreal and complex) and equivalence of the irreducible components (``irrep decompositions’’) of the flavour group representations. In other words, we will derive relations between irrep decompositions and lepton mass patterns, and also between irrep decompositions and possible structures of the PMNS matrix. As we will see, once the decomposition of flavour group representation into irreducible components is specified, one can write down the mass pattern and corresponding form of the mixing matrix without knowing the explicit mass matrix. First we assume that the light neutrino masses are generated by the Weinberg operator, and that the flavour symmetry directly constrains their mass matrix. Under this assumption, we find that there are six viable cases which can account for the approximate description of lepton masses and mixing in the symmetric limit. In all of these cases the neutrino mass spectrum is either inverted hierarchical or the neutrino mass matrix is completely unconstrained (anarchy). In the context of $SU(5)$ unification, only the anarchical option is allowed. Therefore, if the present hint of a normal hierarchical spectrum were confirmed, we would conclude (under the above assumption) that symmetry breaking effects must play a primary role in the understanding of neutrino flavour observables. Then, we consider the case in which light neutrino masses originate from the type I seesaw mechanism and take into account also the transformation properties of the singlet neutrinos under the flavour group. Such a ``high-scale'’ is not always equivalent to the previous ``low-scale’’ analysis. We recover the conditions under which the equivalence of the two analyses necessarily holds. When the two analyses are equivalent, the conclusions obtained in the low-scale analysis hold. Otherwise, the high-scale analysis may provide new results and a normal hierarchy of neutrino masses can be obtained in the symmetric limit. The last part of the thesis is devoted to the new measurements of the anomalous triple gauge boson couplings in the electroweak sector. The goal is to find measurements leading to a large increase of the interference between the SM amplitude and the contributions from $CP$-even dimension six operators in the effective field theory. In particular, in order to overcome non-interference, due to the helicity selection rule, between the amplitudes of the SM and the operator $O_{3W}$ in the tree level process of $q \bar{q}\rightarrow V_TV_T$, in which $V_T$ is transverse polarization state of weak gauge bosons, we propose two distributions that will lead to a better accuracy. The first one is the angular distribution of the interference cross section over the SM one, for the decay of two final state vector bosons. The second one considers a beyond leading order effect from adding one hard jet in the final state. Improvements compared to the traditional methods as well as LHC high luminosity prospects will also be discussed.