Search for the rare 4-body charm decay $D^0 \rightarrow \pi^+ \pi^- \mu^+ \mu^-$ with LHC Run II data

A search for the decay $D^0 \rightarrow \pi^+ \pi^- \mu+ \mu^-$ where the muon pair originates from the $\phi$-resonance region in the di-muon mass spectrum is performed. Proton-proton collison data corresponding to an integrated luminosity of $0.28 \text{fb}^{-1}$ from $2015$ and $0.51 \text{fb}^{-1}$ from $2016$ recorded by the LHCb experiment at a centre-of-mass energy of $13 \text{TeV}$ is examined. A study on trigger efficiences is performed and the results are compared with data recorded by the LHCb experiment at a centre-of-mass energy of $7 \text{TeV}$ corresponding to an integrated luminosity of $2 \text{fb}^{-1}$.