Search for the Higgs boson decay to a pair of electrons in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search is presented for the Higgs boson decay to a pair of electrons in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$. The data set was collected with the CMS experiment at the LHC between 2016 and 2018, corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$. The analysis uses event categories targeting Higgs boson production via gluon-fusion and vector boson fusion. An upper limit on the Higgs boson branching fraction to an electron pair is determined as $3.0\times10^{-4}$ ($3.0\times10^{-4}$ expected) at the $95\%$ confidence level. This is the most stringent limit on the Higgs boson branching fraction to a pair of electrons to date.