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.

Cross sections for the production of a Z boson in association with jets in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 8 TeV are measured using a data sample collected by the CMS experiment at the LHC corresponding to 19.6 inverse femtobarns. Differential cross sections are presented as functions of up to three observables that describe the jet kinematics and the jet activity. Correlations between the azimuthal directions and the rapidities of the jets and the Z boson are studied in detail. The predictions of a number of multileg generators with leading or next-to-leading order accuracy are compared with the measurements. The comparison shows the importance of including multi-parton contributions in the matrix elements and the improvement in the predictions when next-to-leading order terms are included.

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.

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 measurement of the production cross section of top quark pairs in association with two b jets ($\mathrm{t\bar{t}}\mathrm{b\bar{b}}$) is presented using data collected in proton-proton collisions at $\sqrt{s} =$ 13 TeV by the CMS detector at the LHC corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The cross section is measured in the all-jet decay channel of the top quark pair by selecting events containing at least eight jets, of which at least two are identified as originating from the hadronization of b quarks. A combination of multivariate analysis techniques is used to reduce the large background from multijet events not containing a top quark pair, and to help discriminate between jets originating from top quark decays and other additional jets. The cross section is determined for the total phase space to be 5.5 $\pm$ 0.3 (stat)${}^{+1.6}_{-1.3}$ (syst) pb and also measured for two fiducial $\mathrm{t\bar{t}}\mathrm{b\bar{b}}$ definitions. The measured cross sections are found to be larger than theoretical predictions by a factor of 1.5-2.4, corresponding to 1-2 standard deviations.

The production of a Z boson, decaying to two charged leptons, in association with jets in proton-proton collisions at a centre-of-mass energy of 13 TeV is measured. Data recorded with the CMS detector at the LHC are used that correspond to an integrated luminosity of 2.19 fb$^{-1}$. The cross section is measured as a function of the jet multiplicity and its dependence on the transverse momentum of the Z boson, the jet kinematic variables (transverse momentum and rapidity), the scalar sum of the jet momenta, which quantifies the hadronic activity, and the balance in transverse momentum between the reconstructed jet recoil and the Z boson. The measurements are compared with predictions from four different calculations. The first two merge matrix elements with different parton multiplicities in the final state and parton showering, one of which includes one-loop corrections. The third is a fixed-order calculation with next-to-next-to-leading order accuracy for the process with a Z boson and one parton in the final state. The fourth combines the fully differential next-to-next-to-leading order calculation with next-to-next-to-leading logarithm resummation and parton showering.

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 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.