Search for heavy resonances decaying to a $W$ or $Z$ boson and a Higgs boson in final states with leptons and $b$-jets in 36.1~fb$^{-1}$ of $pp$ collision data at $\sqrt s = 13$~\TeV\ with the ATLAS detector

A search is presented for new resonances decaying to a $W$ or $Z$ boson and a 125~\GeV\ Higgs boson (h) in the $\nu\bar{\nu}b\bar{b}$, $\ell^{\pm}{\nu}b\bar{b}$, and $\ell^+\ell^-b\bar{b}$ final states, where $\ell ^{\pm}= e^{\pm}$ or $\mu^{\pm}$, in $pp$ collisions at $\sqrt s = 13$~\TeV. The data used corresponds to a total of 36.1~fb$^{-1}$ of integrated luminosity collected with the ATLAS detector at the Large Hadron Collider from the 2015 and 2016 data taking periods. The search is conducted by examining the reconstructed invariant or transverse mass distributions of $Wh$ and $Zh$ candidates for evidence of a localised excess. The results are interpreted in terms of constraints on the production cross-section times branching fraction of heavy $W^\prime$ and $Z^\prime$ resonances in Heavy Vector Triplet models or the CP odd scalar boson $A$ in Two-Higgs-Doublet models over the mass range from 220 GeV up to 5~TeV. No significant excess is observed. Limits are placed at 95\% CL on the production cross-section times branching fraction and range between $9.0\times 10^{-4}$ and $7.3\times 10^{-1}$~pb depending on the model and mass of the resonance.