Renormalization group equations for theories with axion-like particles via on-shell amplitude methods

In this thesis work, we will carry out the renormalization group equations (RGEs) program in the context of theories with axion-like particles (ALPs). After specifying the ALPs effective field theory, in the first part of this thesis we will evaluate the relevant RGEs through standard one-loop calculations based on Feynman diagram techniques. Instead, the second part of the thesis, which represents an original contribution of the present work, is devoted to reproduce the ALPs RGEs via on-shell amplitude methods, which have been proven to be quite powerful to study the ultraviolet properties of quantum field theories. The ultimate goal of the thesis is to develop a two-loop RGEs program for ALPs theories, which is missing so far in the literature.