Search for the rare decays $B_s^0 \to e^+e^-$ and $B^0 \to e^+e^-$

A search for the decays $B^0_s\to e^+e^-$ and $B^0\to e^+e^-$ is performed using data collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$, $8$ and $13\,\text{TeV}$, corresponding to integrated luminosities of $1$, $2$ and $2\,\text{fb}^{-1}$, respectively. No signal is observed. Assuming no contribution from $B^0\to e^+e^-$ decays, an upper limit of $\mathcal{B}(B^0_s\to e^+e^-)<9.4\,(11.2)\times10^{-9}$ is obtained at $90\,(95)\,\%$ confidence level. If no $B^0_s\to e^+e^-$ contribution is assumed, a limit of $\mathcal{B}(B^0\to e^+e^-)<2.5\,(3.0)\times10^{-9}$ is determined at $90\,(95)\,\%$ confidence level. These upper limits are more than one order of magnitude lower than the previous values.