Signals consistent with the B$^+_\mathrm{c}$(2S) and B$^{*+}_\mathrm{c}$(2S) states are observed in proton-proton collisions at $\sqrt{s} =$ 13 TeV, in an event sample corresponding to an integrated luminosity of 140 fb$^{-1}$, collected by the CMS experiment during the 2016, 2017, and 2018 LHC running periods. These excited $\bar{\mathrm{b}}$c states are observed in the B$^+_\mathrm{c}\pi^+\pi^-$ invariant mass spectrum, with the ground state B$^+_\mathrm{c}$ reconstructed through its decay to J/$\psi\,\pi^+$. The two states are well resolved from each other and are observed with a significance exceeding five standard deviations. The mass of the B$^+_\mathrm{c}$(2S) meson is measured to be 6871.0 $\pm$ 1.2 (stat) $\pm$ 0.8 (syst) $\pm$ 0.8 (B$^+_\mathrm{c}$) MeV, where the last term corresponds to the uncertainty in the world-average B$^+_\mathrm{c}$ mass.

A measurement is presented of electroweak (EW) production of a W boson in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV. The data sample was recorded by the CMS Collaboration at the LHC and corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The measurement is performed for the $\ell\nu$jj final state (with $\ell\nu$ indicating a lepton-neutrino pair, and j representing the quarks produced in the hard interaction) in a kinematic region defined by invariant mass $m_\mathrm{jj}$ $>$ 120 GeV and transverse momenta $p_\mathrm{T j}$ $>$ 25 GeV. The cross section of the process is measured in the electron and muon channels yielding $\sigma_\mathrm{EW}$(Wjj) = 6.23 $\pm$ 0.12 (stat) $\pm$ 0.61 (syst) pb per channel, in agreement with leading-order standard model predictions. The additional hadronic activity of events in a signal-enriched region is studied, and the measurements are compared with predictions. The final state is also used to perform a search for anomalous trilinear gauge couplings. Limits on anomalous trilinear gauge couplings associated with dimension-six operators are given in the framework of an effective field theory. The corresponding 95% confidence level intervals are $-$2.3 $<$ $c_{\mathrm{WWW}}/\Lambda^2$ $<$ 2.5 TeV$^{-2}$, $-$8.8 $<$ $c_{\mathrm{W}}/\Lambda^2$ $<$ 16 TeV$^{-2}$, and $-$45 $<$ $c_{\mathrm{B}}/\Lambda^2$ $<$ 46 TeV$^{-2}$. These results are combined with the CMS EW Zjj analysis, yielding the constraint on the $c_{\mathrm{WWW}}$ coupling: $-$1.8 $<$ $c_{\mathrm{WWW}}/\Lambda^2$ $<$ 2.0 TeV$^{-2}$.

A search for anomalous electroweak production of WW, WZ, and ZZ boson pairs in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV at the LHC is reported. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$ collected with the CMS detector. Events are selected by requiring two jets with large rapidity separation and invariant mass, one or two leptons (electrons or muons), and a W or Z boson decaying hadronically. No excess of events with respect to the standard model background predictions is observed and constraints on the structure of quartic vector boson interactions in the framework of dimension-8 effective field theory operators are reported. Stringent limits on parameters of the effective field theory operators are obtained. The observed 95% confidence level limits for the S0, M0, and T0 operators are $-$2.7 $<$ f$_{\mathrm{S0}}/ \Lambda^{4}$ $<$ 2.7, $-$1.0 $<$ f$_{\mathrm{M0}}/ \Lambda^{4}$ $<$ 1.0, and $-$0.17 $<$ f$_{\mathrm{T0}}/ \Lambda^{4}$ $<$ 0.16, in units of TeV$^{-4}$. Constraints are also reported on the product of the cross section and branching fraction for vector boson fusion production of charged Higgs bosons as a function of mass from 600 to 2000 GeV. The results are interpreted in the context of the Georgi-Machacek model.

A search for supersymmetry is presented based on events with at least one photon, jets, and large missing transverse momentum produced in proton-proton collisions at a center-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 35.9 fb$^{-1}$ and were recorded at the LHC with the CMS detector in 2016. The analysis characterizes signal-like events by categorizing the data into various signal regions based on the number of jets, the number of b-tagged jets, and the missing transverse momentum. No significant excess of events is observed with respect to the expectations from standard model processes. Limits are placed on the gluino and top squark pair production cross sections using several simplified models of supersymmetric particle production with gauge-mediated supersymmetry breaking. Depending on the model and the mass of the next-to-lightest supersymmetric particle, the production of gluinos with masses as large as 2120 GeV and the production of top squarks with masses as large as 1230 GeV are excluded at 95% confidence level.

Measurements of the top quark polarization and top quark pair ($\mathrm{t\bar{t}}$) spin correlations are presented using events containing two oppositely charged leptons (e$^+$e$^-$, e$^\pm\mu^\mp$, or $\mu^+\mu^-$) produced in proton-proton collisions at a center-of-mass energy of 13 TeV. The data were recorded by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A set of parton-level normalized differential cross sections, sensitive to each of the independent coefficients of the spin-dependent parts of the $\mathrm{t\bar{t}}$ production density matrix, is measured for the first time at 13 TeV. The measured distributions and extracted coefficients are compared with standard model predictions from simulations at next-to-leading-order (NLO) accuracy in quantum chromodynamics (QCD), and from NLO QCD calculations including electroweak corrections. All measurements are found to be consistent with the expectations of the standard model. The normalized differential cross sections are used in fits to constrain the anomalous chromomagnetic and chromoelectric dipole moments of the top quark to $-$0.24 $<C_\text{tG}/\Lambda^{2}$ $<$ 0.07 TeV$^{-2}$ and $-$0.33 $< C^{I}_\text{tG}/\Lambda^{2}$ $<$ 0.20 TeV$^{-2}$, respectively, at 95% confidence level.

A search for exotic decays of the Higgs boson to a pair of light pseudoscalar particles a$_1$ is performed under the hypothesis that one of the pseudoscalars decays to a pair of opposite sign muons and the other decays to b$\overline{\mathrm{b}}$. Such signatures are predicted in a number of extensions of the standard model (SM), including next-to-minimal supersymmetry and two-Higgs-doublet models with an additional scalar singlet. The results are based on a data set of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, accumulated with the CMS experiment at the CERN LHC in 2016 at a centre-of-mass energy of 13 TeV. No statistically significant excess is observed with respect to the SM backgrounds in the search region for pseudoscalar masses from 20 GeV to half of the Higgs boson mass. Upper limits at 95% confidence level are set on the product of the production cross section and branching fraction, $\sigma_{\mathrm{h}}\mathcal{B}$(h $\to$ a$_1$ a$_1$ $\to$ $\mu^+\mu^-\mathrm{b}\bar{\mathrm{b}}$), ranging from 5 to 33 fb, depending on the pseudoscalar mass. Corresponding limits on the branching fraction, assuming the SM prediction for $\sigma_{\mathrm{h}}$, are (1$-$7)$\times$ 10$^{-4}$.

A search for supersymmetric particles produced in the vector boson fusion topology in proton-proton collisions is presented. The search targets final states with one or zero leptons, large missing transverse momentum, and two jets with a large separation in rapidity. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} =$ 13 TeV collected in 2016 with the CMS detector at the LHC. The observed dijet invariant mass and lepton-neutrino transverse mass spectra are found to be consistent with the standard model predictions. Upper limits are set on the cross sections for chargino ($\widetilde\chi_1^\pm$) and neutralino ($\widetilde\chi_2^0$) production with two associated jets. For a compressed mass spectrum scenario in which the $\widetilde\chi_1^\pm$ and $\widetilde\chi_2^0$ decays proceed via a light slepton and the mass difference between the lightest neutralino $\widetilde\chi_1^0$ and the mass-degenerate particles $\widetilde\chi_1^\pm$ and $\widetilde\chi_2^0$ is 1 (30) GeV, the most stringent lower limit to date of 112 (215) GeV is set on the mass of these latter two particles.

A top quark mass measurement is performed using 35.9 fb$^{-1}$ of LHC proton-proton collision data collected with the CMS detector at $\sqrt{s} =$ 13 TeV. The measurement uses the $\mathrm{t\overline{t}}$ all-jets final state. A kinematic fit is performed to reconstruct the decay of the $\mathrm{t\overline{t}}$ system and suppress the multijet background. Using the ideogram method, the top quark mass ($m_\mathrm{t}$) is determined, simultaneously constraining an additional jet energy scale factor (JSF). The resulting value of $m_\mathrm{t}$ = 172.34 $\pm$ 0.20 (stat+JSF) $\pm$ 0.70 (syst) GeV is in good agreement with previous measurements. In addition, a combined measurement that uses the $\mathrm{t\overline{t}}$ lepton+jets and all-jets final states is presented, using the same mass extraction method, and provides an $m_\mathrm{t}$ measurement of 172.26 $\pm$ 0.07 (stat+JSF) $\pm$ 0.61 (syst) GeV. This is the first combined $m_\mathrm{t}$ extraction from the lepton+jets and all-jets channels through a single likelihood function.

A search is presented for charged Higgs bosons in the H$^{\pm}$ $\to$ $\tau^{\pm}\nu_\tau$ decay mode in the hadronic final state and in final states with an electron or muon. The search is based on proton-proton collision data recorded by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The results agree with the background expectation from the standard model. Upper limits at 95% confidence level are set on the production cross section times branching fraction to $\tau^{\pm}\nu_\tau$ for an H$^{\pm}$ in the mass range of 80 GeV to 3 TeV, including the region near the top quark mass. The observed limit ranges from 6 pb at 80 GeV to 5 fb at 3 TeV. The limits are interpreted in the context of the minimal supersymmetric standard model $m_\mathrm{h}^\mathrm{mod-}$ scenario.

A general search is presented for a low-mass $\tau^-\tau^+$ resonance produced in association with a bottom quark. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The data are consistent with the standard model expectation. Upper limits at 95% confidence level on the cross section times branching fraction are determined for two signal models: a light pseudoscalar Higgs boson decaying to a pair of $\tau$ leptons produced in association with bottom quarks, and a low-mass boson X decaying to a $\tau$-lepton pair that is produced in the decay of a bottom-like quark B such that B $\to$ bX. Masses between 25 and 70 GeV are probed for the light pseudoscalar boson with upper limits ranging from 250 to 44 pb. Upper limits from 20 to 0.3 pb are set on B masses between 170 and 450 GeV for X boson masses between 20 and 70 GeV.