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Description
Rare semileptonic four-body charm decays such as $D^0\to h^+h^-e^+e^-$ (with $h=\pi,K$) can proceed via long-distance (LD) resonant contributions or short-distance (SD) Flavor Changing Neutral Currents (FCNC) $c\to ue^+e^-$, which are highly suppressed in the Standard Model. These modes are therefore sensitive to potential new physics effects and provide a probe of Lepton Flavour Universality through a comparison with their muonic counterparts $D^0\to h^+h^-\mu^+\mu^-$.
Recently, the LHCb experiment has performed a search for $D^0\to \pi^+\pi^-e^+e^-$ and $D^0\to K^+K^-e^+e^-$ decays using Run 2 data at $\sqrt{s}=13$ TeV collected in 2015-2018 (corresponding to an integrated luminosity of about 6 fb$^{-1}$). The decay $D^0\to \pi^+\pi^-e^+e^-$ was observed for the first time when the dielectron pair is compatible with coming from $\rho(770)$, $\omega(782)$ or $\phi(1020)$ intermediate resonances. The decay $D^0\to K^-\pi^+[e^-e^+]_{\rho/\omega}$ was used as normalization channel. To account for the very different background levels and invariant-mass shapes, the dataset was split into events with and without reconstructed bremsstrahlung associated with the electrons. The measured branching fractions are
$BF(D^0\to\pi^+\pi^-[e^+e^-]_{\rho/\omega}) = (4.5\pm1.0\pm0.7\pm0.6)\times10^{-7}$ and
$BF(D^0\to\pi^+\pi^-[e^+e^-]_{\phi}) = (3.8\pm0.7\pm0.4\pm0.5)\times10^{-7}$.
With the enhanced LHCb trigger capabilities and large collected statistics in Run 3, updated searches and branching-fraction measurements are underway. Preliminary studies on the normalization channel indicate a significant increase in signal yields.