Differential cross sections are measured for the standard model Higgs boson produced in association with vector bosons (W, Z) and decaying to a pair of b quarks. Measurements are performed within the framework of the simplified template cross sections. The analysis relies on the leptonic decays of the W and Z bosons, resulting in final states with 0, 1, or 2 electrons or muons. The Higgs boson candidates are either reconstructed from pairs of resolved b-tagged jets, or from single large distance parameter jets containing the particles arising from two b quarks. Proton-proton collision data at $\sqrt{s}$ = 13 TeV, collected by the CMS experiment in 2016-2018 and corresponding to a total integrated luminosity of 138 fb$^{-1}$, are analyzed. The inclusive signal strength, defined as the product of the observed production cross section and branching fraction relative to the standard model expectation, combining all analysis categories, is found to be $\mu$ = 1.15$^{+0.22}_{-0.20}$. This corresponds to an observed (expected) significance of 6.3 (5.6) standard deviations.

A search for heavy resonances decaying to a $W$ or $Z$ boson and a Higgs boson in the $q\bar{q}^{(\prime)}b\bar{b}$ final state is described. The search uses 36.1 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} =$ 13 TeV collected by the ATLAS detector at the CERN Large Hadron Collider in 2015 and 2016. The data are in agreement with the Standard Model expectations, with the largest excess found at a resonance mass of 3.0 TeV with a local (global) significance of 3.3 (2.1) $\sigma$. The results are presented in terms of constraints on a simplified model with a heavy vector triplet. Upper limits are set on the production cross-section times branching ratio for resonances decaying to a $W$ ($Z$) boson and a Higgs boson, itself decaying to $b\bar{b}$, in the mass range between 1.1 and 3.8 TeV; the limits range between 83 and 1.6 fb (77 and 1.1 fb) at 95% confidence level.

A search is conducted for new resonances decaying into a $W$ or $Z$ boson and a 125 GeV Higgs boson 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 correspond to a total integrated luminosity of 36.1 fb$^{-1}$ collected with the ATLAS detector at the Large Hadron Collider during 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 in the mass range of 220 GeV up to 5 TeV. No significant excess is observed and 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 and the CP-odd scalar boson $A$ in two-Higgs-doublet models. Upper limits are placed at the 95 % confidence level and range between $9.0\times 10^{-4}$ pb and $8.1\times 10^{-1}$ pb depending on the model and mass of the resonance.

A search for a light charged Higgs boson (H$^+$) decaying to a W boson and a CP-odd Higgs boson (A) in final states with e$\mu\mu$ or $\mu\mu\mu$ is performed using data from pp collisions at $\sqrt{s}=$ 13 TeV, recorded by the CMS detector at the LHC and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. In this search, it is assumed that the H$^+$ boson is produced in decays of top quarks, and the A boson decays to two oppositely charged muons. The presence of signals for H$^+$ boson masses between 100 and 160 GeV and A boson masses between 15 and 75 GeV is investigated. No evidence for the production of the H$^+$ boson is found. Upper limits at 95% confidence level are obtained on the combined branching fraction for the decay chain t $\to$ bH$^+$ $\to$ bW$^+$A $\to$ bW$^+\mu^+\mu^-$, of 1.9 $\times$ 10$^{-6}$ to 8.6 $\times$ 10$^{-6}$, depending on the masses of the H$^+$ and A bosons. These are the first limits for these decay modes of the H$^+$ and A bosons.

A search is presented for the pair production of heavy vector-like $T$ and $B$ quarks, primarily targeting the $T$ quark decays to a $W$ boson and a $b$-quark. The search is based on $36.1$ fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, including at least one $b$-tagged jet and a large-radius jet identified as originating from the hadronic decay of a high-momentum $W$ boson. No significant deviation from the Standard Model expectation is observed in the reconstructed $T$ mass distribution. The observed 95% confidence level lower limit on the $T$ mass are 1350 GeV assuming 100% branching ratio to $Wb$. In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. This search is also sensitive to a heavy vector-like $B$ quark decaying to $Wt$ and other final states. The results are thus reinterpreted to provide a 95% confidence level lower limit on the $B$ quark mass at 1250 GeV assuming 100% branching ratio to $Wt$; in the SU(2) singlet scenario, the limit is 1080 GeV. Mass limits on both $T$ and $B$ production are also set as a function of the decay branching ratios. The 100% branching ratio limits are found to be applicable to heavy vector-like $Y$ and $X$ production that decay to $Wb$ and $Wt$, respectively.

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 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 GeV for the $A$ boson and 130-700 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 $\sigma \times B(A\rightarrow ZH) \times B(H\rightarrow bb$ or $H\rightarrow WW)$ are set. The upper limits are in the range 0.0062-0.380 pb for the $H\rightarrow bb$ channel and in the range 0.023-8.9 pb for the $H\rightarrow WW$ channel. An interpretation of the results in the context of two-Higgs-Doublet models is also given.