A measurement is presented of the production of Z bosons that decay into two electrons or muons in association with jets, in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data were recorded by the CMS Collaboration at the LHC with an integrated luminosity of 35.9 fb$^{-1}$. The differential cross sections are measured as a function of the transverse momentum ($p_\mathrm{T}$) of the Z boson and the transverse momentum and rapidities of the five jets with largest $p_\mathrm{T}$. The jet multiplicity distribution is measured for up to eight jets. The hadronic activity in the events is estimated using the scalar sum of the $p_\mathrm{T}$ of all the jets. All measurements are unfolded to the stable particle-level and compared with predictions from various Monte Carlo event generators, as well as with expectations at leading and next-to-leading orders in perturbative quantum chromodynamics.

A first observation is presented for the electroweak production of a W boson, a photon, and two jets in proton-proton collisions. The W boson decays are selected by requiring one identified electron or muon and an imbalance in transverse momentum. The two jets are required to have a high dijet mass and a large separation in pseudorapidity. The measurement is based on data collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results at 8 TeV, the observed (expected) significance is 5.3 (4.8) standard deviations. The cross section for the electroweak W$\gamma$jj production in a restricted fiducial region is measured as 20.4 $\pm$ 4.5 fb and the total cross section for W$\gamma$ production in association with 2 jets in the same fiducial region is 108 $\pm$ 16 fb. All results are in good agreement with recent theoretical predictions. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-8 effective field theory operators.

Evidence is presented for the electroweak (EW) production of two jets (jj) in association with two Z bosons and constraints on anomalous quartic gauge couplings are set. The analysis is based on a data sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV collected with the CMS detector in 2016-2018, and corresponding to an integrated luminosity of 137 fb$^{-1}$. The search is performed in the fully leptonic final state ZZ $\to$ $\ell\ell\ell'\ell'$, where $\ell,\ell' = $ e, $\mu$. The EW production of two jets in association with two Z bosons is measured with an observed (expected) significance of 4.0 (3.5) standard deviations. The cross sections for the EW production are measured in three fiducial volumes and the result is $\sigma_{\mathrm{EW}}$(pp $\to$ ZZjj $\to$ $\ell\ell\ell'\ell'$jj) = 0.33 $^{+0.11}_{-0.10}$ (stat) $^{+0.04}_{-0.03}$ (syst) fb in the most inclusive volume, in agreement with the standard model prediction of 0.275 $\pm$ 0.021 fb. Measurements of total cross sections for jj production in association with two Z bosons are also reported. Limits on anomalous quartic gauge couplings are derived in terms of the effective field theory operators T0, T1, T2, T8, and T9.

A search is performed for W' bosons decaying to a top and a bottom quark in the all-hadronic final state, in proton-proton collisions at a center-of-mass energy of 13 TeV. The analyzed data were collected by the CMS experiment between 2016 and 2018 and correspond to an integrated luminosity of 137 fb$^{-1}$. Deep neural network algorithms are used to identify the jet initiated by the bottom quark and the jet containing the decay products of the top quark when the W boson from the top quark decays hadronically. No excess above the estimated standard model background is observed. Upper limits on the production cross sections of W' bosons decaying to a top and a bottom quark are set. Both left- and right-handed W' bosons with masses below 3.4 TeV are excluded at 95% confidence level, and the most stringent limits to date on W' bosons decaying to a top and a bottom quark in the all-hadronic final state are obtained.

A measurement of the cross section of the associated production of a single top quark and a W boson in final states with a muon or electron and jets in proton-proton collisions at $\sqrt{s}$ = 13 TeV is presented. The data correspond to an integrated luminosity of 36 fb$^{-1}$ collected with the CMS detector at the CERN LHC in 2016. A boosted decision tree is used to separate the tW signal from the dominant $\mathrm{t\bar{t}}$ background, whilst the subleading W+jets and multijet backgrounds are constrained using data-based estimates. This result is the first observation of the tW process in final states containing a muon or electron and jets, with a significance exceeding 5 standard deviations. The cross section is determined to be 89 $\pm$ 4 (stat) $\pm$ 12 (syst) pb, consistent with the standard model.

The first observation of the electroweak (EW) production of a Z boson, a photon, and two forward jets (Z$\gamma$jj) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. A data set corresponding to an integrated luminosity of 137 fb$^{-1}$, collected by the CMS experiment at the LHC in 2016-2018 is used. The measured fiducial cross section for EW Z$\gamma$jj is $\sigma_{\mathrm{EW}}$ = 5.21 $\pm$ 0.52 (stat) $\pm$ 0.56 (syst) fb = 5.21 $\pm$ 0.76 fb. Single-differential cross sections in photon, leading lepton, and leading jet transverse momenta, and double-differential cross sections in $m_{\mathrm{jj}}$ and $\lvert\Delta\eta_{\mathrm{jj}}\rvert$ are also measured. Exclusion limits on anomalous quartic gauge couplings are derived at 95% confidence level in terms of the effective field theory operators $\mathrm{M}_{0}$ to $\mathrm{M}_{5}$, $\mathrm{M}_{7}$, $\mathrm{T}_{0}$ to $\mathrm{T}_{2}$, and $\mathrm{T}_{5}$ to $\mathrm{T}_{9}$.

A search for resonances decaying into a W boson and a radion, where the radion decays into two W bosons, is presented. The data analyzed correspond to an integrated luminosity of 138 fb$^{-1}$ recorded in proton-proton collisions with the CMS detector at $\sqrt{s} =$ 13 TeV. One isolated charged lepton is required, together with missing transverse momentum and one or two massive large-radius jets, containing the decay products of either two or one W bosons, respectively. No excess over the background estimation is observed. The results are combined with those from a complementary channel with an all-hadronic final state, described in an accompanying paper. Limits are set on parameters of an extended warped extra-dimensional model. These searches are the first of their kind at the LHC.

A search for Kaluza-Klein excited vector boson resonances, $W_\mathrm{KK}$, decaying in cascade to three W bosons via a scalar radion $R, W_\mathrm{KK}\to WR \to WWW$, with two or three massive jets is presented. The search is performed with proton-proton collision data recorded at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment at the CERN LHC, during 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. Two final states are simultaneously probed, one where the two W bosons produced by the R decay are reconstructed as separate, large-radius, massive jets, and one where they are merged in a single large-radius jet. The observed data are in agreement with the standard model expectations. Limits are set on the product of the $W_\mathrm{KK}$ resonance cross section and branching fraction to three W bosons in an extended warped extra-dimensional model and are the first of their kind at the LHC.

The observation of the standard model (SM) Higgs boson decay to a pair of bottom quarks is presented. The main contribution to this result is from processes in which Higgs bosons are produced in association with a W or Z boson (VH), and are searched for in final states including 0, 1, or 2 charged leptons and two identified bottom quark jets. The results from the measurement of these processes in a data sample recorded by the CMS experiment in 2017, comprising 41.3 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} =$ 13 TeV, are described. When combined with previous VH measurements using data collected at $\sqrt{s}=$ 7, 8, and 13 TeV, an excess of events is observed at $m_\mathrm{H} =$ 125.09 GeV with a significance of 4.8 standard deviations, where the expectation for the SM Higgs boson is 4.9. The corresponding measured signal strength is 1.01 $\pm$ 0.22. The combination of this result with searches by the CMS experiment for H $\to\mathrm{b\overline{b}}$ in other production processes yields an observed (expected) significance of 5.6 (5.5) standard deviations and a signal strength of 1.04 $\pm$ 0.20.

A search is presented for pairs of light pseudoscalar bosons, in the mass range from 4 to 15 GeV, produced from decays of the 125 GeV Higgs boson. The decay modes considered are final states that arise when one of the pseudoscalars decays to a pair of tau leptons, and the other one either into a pair of tau leptons or muons. The search is based on proton-proton collisions collected by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV that correspond to an integrated luminosity of 35.9 fb${-1}$. The 2$\mu$2$\tau$ and 4$\tau$ channels are used in combination to constrain the product of the Higgs boson production cross section and the branching fraction into 4$\tau$ final state, $\sigma\mathcal{B}$, exploiting the linear dependence of the fermionic coupling strength of pseudoscalar bosons on the fermion mass. No significant excess is observed beyond the expectation from the standard model. The observed and expected upper limits at 95% confidence level on $\sigma\mathcal{B}$, relative to the standard model Higgs boson production cross section, are set respectively between 0.022 and 0.23 and between 0.027 and 0.19 in the mass range probed by the analysis.