This thesis presents the first-ever study of the decay of a neutral kaon into four muons. Using data collected by the LHCb experiment between 2016 and 2018, no signal was found, and stringent upper limits on the branching fractions of both the short- and long-lived modes were set.
Additionally, the study of four decays of eta and eta prime mesons are presented. The thesis introduces the first-ever study of the eta prime decaying into a pair of muons, as well as significant improvements on the precision of the branching fractions of the di-muon decay of the eta, as well as the decays of both the eta and eta prime mesons into two pairs of muons and two pairs of pions.
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