Search for a heavy charged Higgs boson decaying into a $W$ boson and a Higgs boson in final states with leptons and $b$-jets in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

This article presents a search for a heavy charged Higgs boson produced in association with a top quark and a bottom quark, and decaying into a $W$ boson and a $125$ GeV Higgs boson $h$. The search is performed in final states with one charged lepton, missing transverse momentum, and jets using proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector during Run 2 of the LHC at CERN. This data set corresponds to a total integrated luminosity of 140 fb${}^{-1}$. The search is conducted by examining the reconstructed invariant mass distribution of the $Wh$ candidates for evidence of a localised excess in the charged Higgs boson mass range from $250$ GeV to $3$ TeV. No significant excess is observed and 95% confidence-level upper limits between $2.8$ pb and $1.2$ fb are placed on the production cross-section times branching ratio for charged Higgs bosons decaying into $Wh$.