Search for the flavour-changing neutral-current decay $D^0 \to \mu^{+}\mu^{-}$

We have searched for the decay $D^0 \rightarrow \mu^+\mu^-$ among $2.0 \times 10^5$ $\mu^+\mu^-$ pairs \hbox{produced,} in the WA92 experiment, by 350 GeV/$c$ \ $\pi^-$ particles interacting in copper and tungsten targets. \hbox{Using} a high-resolution silicon-microstrip detector followed by a large-acceptance magnetic spectrometer and a muon filter we are able to measure the momentum of the muons, to visualize the event topology near their point of origin, and thus to discriminate between prompt and non-prompt muons. No $D^0 \rightarrow \mu^+\mu^-$ candidate has been found. This result allows us to set an upper limit on the branching fraction \hbox {B$(D^0 \rightarrow \mu^+\mu^-)$} of $ 4.1 \times 10^{-6}$ at 90 \% confidence level.