First observation of the decay $D^*( 2007 )^0\to D^0 e^+e^-$ in the light of a future Dark Photon search at the LHCb experiment

In this thesis, the first observation of the decay $D^∗( 2007 )^0\to D^0e^+e^−$ and a measurement of its branching ratio relative to the decay $D^∗( 2007 )^0\to D^0γ$ is performed. The dataset was collected by the LHCb experiment in proton-proton collisions at 13 TeV centre-of-mass energy in 2017 and corresponds to an integrated luminosity of approximately 1.87 $fb^{−1}$ . In total, 3253 ± 238 $D^∗( 2007 )^0\to D^0e^+e^−$ decays are reconstructed and selected, leading to a statistical significance of 12.7 standard deviations. The result of the relative branching fraction measurement is ( 9.6 ± 0.7 ( stat ) ± 2.3 ( syst )) × 10$^{−3}$ , where the uncertainties are statistical and systematic, respectively. From this, the branching ratio of the decay $D^∗( 2007 )^0\to D^0e^+e^−$ is inferred to be ( 3.38 ± 0.25 ( stat ) ± 0.82 ( syst ) ± 0.09 ) × $10^{−3}$, where the third uncertainty is due to the uncertainty on the branching fraction of the normalisation channel $D^∗( 2007 )^0\to D^0γ$.