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Searches for the Higgs boson decays $H \to ee$ and $H \to e \mu$ areperformed using data corresponding to an integrated luminosity of 139 fb$^{-1}$collected with the ATLAS detector in $pp$ collisions at $\sqrt{s} = 13$ TeV atthe LHC. No significant signals are observed, in agreement with the StandardModel expectation. For a Higgs boson mass of 125 GeV, the observed (expected)upper limit at the 95% confidence level on the branching fraction$\mathcal{B}(H \to ee)$ is $3.6 \times 10^{-4}$ ($3.5 \times 10^{-4} $) and on$\mathcal{B}(H \to e \mu)$ is $6.1\times 10^{-5} $ ($5.8\times 10^{-5}$). Theseresults represent improvements by factors of about five and six on the previousbest limits on $\mathcal{B}(H \to ee)$ and $\mathcal{B}(H \to e \mu)$respectively.

Search for the Higgs boson decays $H \to ee$ and $H \to e\mu$ in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector