A search for pair production of doubly charged Higgs bosons ($H^{\pm \pm}$), each decaying into a pair of prompt, isolated, highly energetic leptons with the same electric charge, is presented. The search uses a proton-proton collision data sample at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb$^{-1}$ recorded by the ATLAS detector during Run 2 of the Large Hadron Collider. This analysis focuses on same-charge leptonic decays, $H^{\pm \pm} \rightarrow \ell^{\pm} \ell^{\prime \pm}$ where $\ell, \ell^\prime=e, \mu, \tau$, in two-, three-, and four-lepton channels, but only considers final states which include electrons or muons. No evidence of a signal is observed. Corresponding limits on the production cross-section and consequently a lower limit on $m(H^{\pm \pm})$ are derived at 95% confidence level. Assuming that the branching ratios to each of the possible leptonic final states are equal, $\mathcal{B}(H^{\pm \pm} \rightarrow e^\pm e^\pm) = \mathcal{B}(H^{\pm \pm} \rightarrow e^\pm \mu^\pm) = \mathcal{B}(H^{\pm \pm} \rightarrow \mu^\pm \mu^\pm) = \mathcal{B}(H^{\pm \pm} \rightarrow e^\pm \tau^\pm) = \mathcal{B}(H^{\pm \pm} \rightarrow \mu^\pm \tau^\pm) = \mathcal{B}(H^{\pm \pm} \rightarrow \tau^\pm \tau^\pm) = 1/6$, the observed lower limit on the mass of a doubly charged Higgs boson is 1080 GeV within the left-right symmetric type-II seesaw model, which is an improvement over previous limits. Additionally, a lower limit of $m(H^{\pm \pm})$ = 900 GeV is obtained in the context of the Zee-Babu neutrino mass model.
LO, NLO cross-sections and K-factors for the pair-production of doubly charged Higgs bosons in pp collisions at $\sqrt{s}$ = 13 TeV. The K-factors (K=$\sigma_{NLO}/\sigma_{LO}$) are identical for $H^{\pm\pm}_L$, $H^{\pm\pm}_R$, and $k^{\pm\pm}$. The values are calculated using the NNPDF3.1NLO and NNPDF2.3LO PDF sets.
Observed (solid line) and expected (dashed line) 95% CL upper limits on the $H^{\pm\pm}$ pair production cross-section as a function of $m(H^{\pm\pm})$ resulting from the combination of all analysis channels, assuming $\sum_{\ell \ell^\prime} \mathcal{B}(H^{\pm\pm} \rightarrow \ell^{\pm} \ell^{\prime \pm})=100%$, where $\ell, \ell^\prime = e, \mu, \tau$.
Distribution of $m(e^{\pm},e^{\pm})_{\mathrm{lead}}$ in the electron-electron signal region after the background-only fit.
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