Search for a charged Higgs boson decaying into a heavy neutral Higgs boson and a W boson in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search for a charged Higgs boson $\mathrm{H^{\pm}}$ decaying into a heavy neutral Higgs boson $\mathrm{H}$ and a $\mathrm{W}$ boson is presented. The analysis targets the $\mathrm{H}$ boson decay into a pair of tau leptons with at least one of them decaying hadronically and with an additional electron or muon present in the event. The search is based on proton-proton collision data recorded by the CMS experiment during 2016$-$2018 at $\sqrt{s} = 13~\mathrm{TeV}$, corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$. The observed data are consistent with standard model expectations. Upper limits at $95\%$ confidence level are set on the product of the cross section and branching fraction for an $\mathrm{H^{\pm}}$ in the mass range of 300 to $700~\mathrm{GeV}$, assuming an $\mathrm{H}$ with a mass of $200~\mathrm{GeV}$. The observed limit ranges from $0.080~\mathrm{pb}$ at 300$~\mathrm{GeV}$ to $0.013~\mathrm{pb}$ at $700~\mathrm{GeV}$. These are the first limits on this process at the LHC.