Search for heavy resonances decaying into a $Z$ or $W$ boson and a Higgs boson in final states with leptons and $b$-jets in $139~$fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13~$TeV with the ATLAS detector

This article presents a search for new resonances decaying into a Z or W boson and a 125 GeV Higgs boson h, and it targets the v (v) over barb (b) over bar, l(+)l(-) b (b) over bar, or l(+/-) vb (b) over bar final states, where l - e or mu, in proton-proton collisions at root s - 13 TeV. The data used correspond to a total integrated luminosity of 139 fb(-1) collected by the ATLAS detector during Run 2 of the LHC at CERN. The search is conducted by examining the reconstructed invariant or transverse mass distributions of Zh or Wh candidates for evidence of a localised excess in the mass range from 220 GeV to 5TeV. No significant excess is observed and 95% confidence-level upper limits between 1.3 pb and 0.3 fb are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances and CP-odd scalar bosons. These limits are converted into constraints on the parameter space of the Heavy Vector Triplet model and the two-Higgs-doublet model.