Feasibility study of $K^0_{\rm S} \to \pi^+\pi^-e^+e^-$ at LHCb

The feasibility of observing the $K^0_{\rm S} \to \pi^+\pi^-e^+e^-$ decay at LHCb is studied using simulated and real data. During the Run I of the LHC, the yield of events expected per $\text {fb}^{-1}$ of $pp$ collisions at $\sqrt s=8~ \text {TeV}$ is found to be $N _{RunI}(K^0_{\rm S} \to \pi^+\pi^-e^+e^-) = 120^{+280}_ {-100}$. A dedicated trigger selection has been developed for the 2016 data-taking. The expected yield per $\text {fb}^{-1}$ in Run II is found to be $N _{RunII}(K^0_{\rm S} \to \pi^+\pi^-e^+e^-) = 120^{+280}_ {-100}$. A large signal yield, $N_{Upgrade}(K^0_{\rm S} \to \pi^+\pi^-e^+e^-) = (5.0 \pm 0.3) \times 10^4$ per $\text {fb}^{-1}$, is expected in the LHC upgrade phase. In the Run I data, the signal over background ratio is too low to observe the signal without any additional selection. The observation of this decay with this dataset would require the development of a further high-efficiency large-rejection selection, which is out of the scope of the present study.