ETD

• Dark Matter
• freeze-in
• KS test
• Lepton flavour violation
• MEG II
• muon decay

This thesis presents a sensitivity study for the charged-lepton-flavour-violating decay μ⁺→e⁺χχ̄, where χ is a light Dirac fermion dark matter candidate, in the context of the MEG II experiment. Unlike previous studies of two-body invisible decays (μ⁺→e⁺a), this work considers dimension‑six four‑fermion operators inducing a genuine three‑body decay. The positron energy and angular distributions differ from the Michel background, providing experimental handles. The effective operators are classified and used to compute the freeze‑in production of χ. A critical reheating temperature is identified below which dark matter production is dominated by the decay μ→eχχ̄, making the relic density directly related to the low‑energy operator probed by MEG II. Experimentally, a dedicated Monte Carlo simulation of the signal is integrated into the MEG II framework. A Kolmogorov‑Smirnov test determines the minimum detectable branching ratio, translating into a reach on the new‑physics scale Λ of a few TeV. The analysis is applied to real 2021‑2022 data, and extrapolation to the full MEG II dataset (including 2026) improves the sensitivity. This work establishes μ⁺→e⁺χχ̄ as a well‑motivated probe connecting flavour violation, dark matter, and freeze‑in cosmology.