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 protonproton collisions at centerofmass 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.
Simultaneous fit to the dielectron invariantmass distribution, with $\mathcal{B}( B ^0 \rightarrow e ^+ e ^ )$ fixed to zero. The sum of bremsstrahlung categories is shown for (left) Run 1 and (right) Run 2. The relative proportions of background contributions change between Run 1 and Run 2 due to different performances of the particle identification algorithms and BDT selections. 
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CL$_s$ values as a function of the branching fractions of the decays (left) $ B ^0_ s \rightarrow e ^+ e ^ $ and (right) $ B ^0 \rightarrow e ^+ e ^ $ . The red solid line (black solid line with data points) corresponds to the distribution of the expected (observed) upper limits, and the light blue (dark blue) band contains the $1\sigma$ $(2\sigma)$ uncertainties on the expected upper limits. Thresholds corresponding to $90 \%$ and $95 \%$ confidence level are indicated with dashed lines. The observed values are plotted for branching fractions greater than the measured branching fraction in the data; the test statistic is defined to be nonzero only in that region. 
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Simultaneous fit to the dielectron invariantmass distribution in all categories, with $\mathcal{B}( B ^0 \rightarrow e ^+ e ^ )$ fixed to zero. The top figures show the three bremsstrahlung categories in the Run 1 data set and the bottom figures show the Run 2 data set. From left to right, the data sets correspond to the bremsstrahlung correction category with no correction, correcting one electron and correcting both electrons. The relative proportions of background contributions change between Run 1 and Run 2 due to different performances of the particleidentification algorithms and BDT selections. Their relative fractions between bremsstrahlung categories follow the expectation from simulation. 
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Simultaneous fit to the dielectron invariantmass distribution, with $\mathcal{B}( B ^0_ s \rightarrow e ^+ e ^ )$ fixed to zero. The bremsstrahlung categories are summed over the (left) Run 1 and (right) Run 2 data sets. The relative proportions of background contributions change between Run 1 and Run 2 due to different performances of the particleidentification algorithms and BDT selections. 
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Simultaneous fit to the dielectron invariantmass distribution in all categories, with $\mathcal{B}( B ^0_ s \rightarrow e ^+ e ^ )$ fixed to zero. The top figures show the three bremsstrahlung categories in the Run 1 data set and the bottom figures show the Run 2 data set. From left to right, the data sets correspond to the bremsstrahlung correction category with no correction, correcting one electron and correcting both electrons. The relative proportions of background contributions change between Run 1 and Run 2 due to different performances of the particleidentification algorithms and BDT selections. Their relative fractions between bremsstrahlung categories follow the expectation from simulation. 
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Animated gif made out of all figures. 
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Normalization factors $\alpha$ for $ B _{( s )}^0 \rightarrow e ^+ e ^ $ . The bremsstrahlung category denotes whether zero, one or both electrons are corrected for bremsstrahlung losses. The uncertainties include statistical uncertainties and uncertainties due to limited size of the simulated samples. 
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Inputs for the normalization factors, the efficiency ratio $\varepsilon( B ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ )/\varepsilon( B _{( s )}^0 \rightarrow e ^+ e ^ )$ and normalization yield $N( B ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ )$. The bremsstrahlung category (Brem. cat.) denotes whether zero, one or both electrons are corrected for bremsstrahlung losses. The uncertainties on the efficiency ratios include statistical uncertainties from the calibration and uncertainties due to limited size of the simulated samples. 
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Created on 06 March 2021.