Effective Field Theory tools for investigating physics Beyond the Standard Model

Effective field theories (EFTs) represent the ideal framework where to theoretically investigate physics beyond the Standard Model (SM) in the most agnostic way possible. Wide varieties of well-motivated UV completions of the SM, formulated at energies above the electroweak scale, reduce to the same EFT universality class at lower energies. Quantitative analyses of the impact that EFT operators have on experimental observables can be used to discriminate between different UV models. In view of this, it is of paramount importance to develop new tools to perform coherent and comprehensive EFT analyses in an efficient way. In this thesis, some of the EFT tools I have developed in my doctoral research are going to be presented. One of these consists in a significant generalization of an on-shell, unitarity-based method for efficiently computing the renormalization group equations (RGEs) of general quantum field theories. Our generalization allows for the inclusion of general operator mixing and leading mass effects, which could not be described in the standard formulation of the method. Another research line regards the construction of low-energy effective Lagrangians for light new physics candidates. Within this direction, my works mainly address the inclusion of axion-like particles within the context of chiral perturbation theory. In the second half of this thesis, phenomenological applications of these EFT tools are illustrated in the context of CP-violating axion-like particles (ALPs) through the study of electric dipole moments (EDMs) of particles, nucleons, nuclei and molecules.