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 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 cross section of top quark pair production is measured in the $\mathrm{t\bar{t}}\to (\ell\nu_{\ell})(\tau_\mathrm{h}\nu_{\tau})\mathrm{b\bar{b}}$ final state, where $\tau_\mathrm{h}$ refers to the hadronic decays of the $\tau$ lepton, and $\ell$ is either an electron or a muon. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$ collected in proton-proton collisions at $\sqrt{s}=$ 13 TeV with the CMS detector. The measured cross section is $\sigma_{\mathrm{t\bar{t}}} =$ 781 $\pm$ 7 (stat) $\pm$ 62 (syst) $\pm$ 20 (lum) pb, and the ratio of the partial width $\Gamma($t$\to\tau\nu_{\tau}$b) to the total decay width of the top quark is measured to be 0.1050 $\pm$ 0.0009 (stat) $\pm$ 0.0071 (syst). This is the first measurement of the $\mathrm{t\bar{t}}$ production cross section in proton-proton collisions at $\sqrt{s}=$ 13 TeV that explicitly includes $\tau$ leptons. The ratio of the cross sections in the $\ell\tau_\mathrm{h}$ and $\ell\ell$ final states yields a value $R_{\ell\tau_\mathrm{h}/\ell\ell}=$ 0.973 $\pm$ 0.009 (stat) $\pm$ 0.066 (syst), consistent with lepton universality.

A measurement is presented of the cross section for electroweak production of a Z boson and a photon in association with two jets (Z$\gamma$jj) in proton-proton collisions. The Z boson candidates are selected through their decay into a pair of electrons or muons. The process of interest, electroweak Z$\gamma$jj production, is isolated by selecting events with a large dijet mass and a large pseudorapidity gap between the two jets. The measurement is based on data collected at the CMS experiment at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed significance of the signal is 3.9 standard deviations, where a significance of 5.2 standard deviations is expected in the standard model. These results are combined with published results by CMS at $\sqrt{s} =$ 8 TeV, which leads to observed and expected respective significances of 4.7 and 5.5 standard deviations. From the 13 TeV data, a value is obtained for the signal strength of electroweak Z$\gamma$jj production and bounds are given on quartic vector boson interactions in the framework of dimension-eight effective field theory operators.

The fiducial cross section for $\Upsilon$(1S) pair production in proton-proton collisions at a center-of-mass energy of 13 TeV in the region where both $\Upsilon$(1S) mesons have an absolute rapidity below 2.0 is measured to be 79 $\pm$ 11 (stat) $\pm$ 6 (syst) $\pm$ 3 ($\mathcal{B}$) pb assuming the mesons are produced unpolarized. The last uncertainty corresponds to the uncertainty in the $\Upsilon$(1S) meson dimuon branching fraction. The measurement is performed in the final state with four muons using proton-proton collision data collected in 2016 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. This process serves as a standard model reference in a search for narrow resonances decaying to $\Upsilon$(1S)$\mu^+\mu^-$ in the same final state. Such a resonance could indicate the existence of a tetraquark that is a bound state of two b quarks and two $\bar{\mathrm{b}}$ antiquarks. The tetraquark search is performed for masses in the vicinity of four times the bottom quark mass, between 17.5 and 19.5 GeV, while a generic search for other resonances is performed for masses between 16.5 and 27 GeV. No significant excess of events compatible with a narrow resonance is observed in the data. Limits on the production cross section times branching fraction to four muons via an intermediate $\Upsilon$(1S) resonance are set as a function of the resonance mass.

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.