Search for a heavy Higgs boson decaying into a Z boson and another heavy Higgs boson in the $\ell \ell bb$ and $\ell \ell WW$ final states in pp collisions at $\sqrt{s}=13$ $\text{TeV}$ with the ATLAS detector

A search for a heavy neutral Higgs boson, A, decaying into a Z boson and another heavy Higgs boson, H, is performed using a data sample corresponding to an integrated luminosity of 139 fb ${}^{-1}$ from proton–proton collisions at $\sqrt{s}=13$ $\text{TeV}$ recorded by the ATLAS detector at the LHC. The search considers the Z boson decaying into electrons or muons and the H boson into a pair of b-quarks or W bosons. The mass range considered is 230–800 $\text{GeV}$ for the A boson and 130–700 $\text{GeV}$ for the H boson. The data are in good agreement with the background predicted by the Standard Model, and therefore 95% confidence-level upper limits for $\sigma ×B\left(A\to ZH\right)×B\left(H\to bb\phantom{\rule{0.277778em}{0ex}}\text{or}\phantom{\rule{0.277778em}{0ex}}H\to WW\right)$ are set. The upper limits are in the range 0.0062–0.380 pb for the $H\to bb$ channel and in the range 0.023–8.9 pb for the $H\to WW$ channel. An interpretation of the results in the context of two-Higgs-doublet models is also given.