• axion-like particles
• cLFV
• McMule
• MEG II
• muon decay
• radiative corrections

The Standard Model (SM) provides a comprehensive description of the fundamental constituents of matter and their interactions. In addition to the on-shell production of new particles in high-energy collisions, the search for signals beyond the SM can be pursued through precision measurements of flavour physics. In this context, the MEG II experiment at PSI searches the charged Lepton Flavour Violating (cLFV) decay mu -> e gamma employing a continuous beam of 3*10^7 mu/s. Furthermore, MEG II appears to be competitive in searching more exotic processes, in which the lepton flavour violation is mediated by a light scalar boson X^0, which may be identified as a pseudo-Goldstone boson arising from a spontaneous breaking of a global U(1) symmetry. The search for such axion-like particles (ALPs) is an unique opportunity for MEG II to complement its main search with additional physics channels. The aim of this thesis is to study the feasibility of searching the two-body decay mu -> e X with MEG II, addressing both the theoretical and the experimental difficulties of hunting such an elusive signal. Since the light particle X cannot be detected, the only signature is a monochromatic signal in the high-energy region of the positron spectrum, which has to be reconstructed with the highest precision possible. Hence, an accurate theoretical evaluation of the SM background as well as an exhaustive Monte Carlo simulation of the experiment are essential. Both are goals of this thesis.