The $\chi_\mathrm{b1}$(3P) and $\chi_\mathrm{b2}$(3P) states are observed through their $\Upsilon$(3S) $\gamma$ decays, using an event sample of proton-proton collisions collected by the CMS experiment at the CERN LHC. The data were collected at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 80.0 fb$^{-1}$. The $\Upsilon$(3S) mesons are identified through their dimuon decay channel, while the low-energy photons are detected after converting to e$^+$e$^-$ pairs in the silicon tracker, leading to a $\chi_\mathrm{b}$(3P) mass resolution of 2.2 MeV. This is the first time that the $J =$ 1 and 2 states are well resolved and their masses individually measured: 10$\,$513.42 $\pm$ 0.41 (stat) $\pm$ 0.18 (syst) MeV and 10$\,$524.02 $\pm$ 0.57 (stat) $\pm$ 0.18 (syst) MeV; they are determined with respect to the world-average value of the $\Upsilon$(3S) mass, which has an uncertainty of 0.5 MeV. The mass splitting is measured to be 10.60 $\pm$ 0.64 (stat) $\pm$ 0.17 (syst) MeV.

A search for the pair production of resonances, each decaying to two quarks, is reported. The search is conducted separately for heavier resonances (masses above 400 GeV), where each of the four final-state quarks generates a hadronic jet resulting in a four-jet signature, and for lighter resonances (masses between 80 and 400 GeV), where the pair of quarks from each resonance is collimated and reconstructed as a single jet resulting in a two-jet signature. In addition, a b-tagged selection is applied to target resonances with a bottom quark in the final state. The analysis uses data collected with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$, from proton-proton collisions at a center-of-mass energy of 13 TeV. The mass spectra are analyzed for the presence of new resonances, and are found to be consistent with standard model expectations. The results are interpreted in the framework of $R$-parity-violating supersymmetry assuming the pair production of scalar top quarks decaying via the hadronic coupling $\lambda_{312}"$ or $\lambda_{323}"$, and upper limits on the cross section as a function of the top squark mass are set. These results probe lower masses than previously explored at the LHC, and extend the top squark mass limits in the $\widetilde{\mathrm{t}}$$\to$qq$'$ scenario.

A search for exotic Higgs boson decays to light pseudoscalars in the final state of two muons and two $\tau$ leptons is performed using proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Masses of the pseudoscalar boson between 15.0 and 62.5 GeV are probed, and no significant excess of data is observed above the prediction of the standard model. Upper limits are set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different types of two-Higgs-doublet models extended with a complex scalar singlet.

A measurement of the electroweak (EW) production of two jets in association with a Z boson in proton-proton collisions at $\sqrt{s} = $ 13 TeV is presented, based on data recorded in 2016 by the CMS experiment at the LHC corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The measurement is performed in the $\ell\ell\mathrm{jj}$ final state with $\ell$ including electrons and muons, and the jets j corresponding to the quarks produced in the hard interaction. The measured cross section in a kinematic region defined by invariant masses $m_{\ell\ell} > $ 50 GeV, $m_{\mathrm{jj}} > $ 120 GeV, and transverse momenta $p_{\mathrm{T j}} > $ 25 GeV is $\sigma_\mathrm{EW}(\ell\ell\mathrm{jj})= $ 552 $\pm$ 19 (stat) $\pm$ 55 (syst) fb, in agreement with leading-order standard model predictions. The final state is also used to perform a search for anomalous trilinear gauge couplings. No evidence is found and 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 $-2.6 < c_{WWW}/\Lambda^2 < 2.6 $ TeV$^{-2}$ and $-8.4 < c_{W}/\Lambda^2 < 10.1 $ TeV$^{-2}$. The additional jet activity of events in a signal-enriched region is also studied, and the measurements are in agreement with predictions.

The angular distribution of the flavor-changing neutral current decay B$^+$$\to$ K$^+\mu^+\mu^-$ is studied in proton-proton collisions at a center-of-mass energy of 8 TeV. The analysis is based on data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb$^{-1}$. The forward-backward asymmetry $A_{\mathrm{FB}}$ of the dimuon system and the contribution $F_{\mathrm{H}}$ from the pseudoscalar, scalar, and tensor amplitudes to the decay width are measured as a function of the dimuon mass squared. The measurements are consistent with the standard model expectations.

Three of the most significant measured deviations from standard model predictions, the enhanced decay rate for B $\to$ D$^{(*)}\tau\nu$, hints of lepton universality violation in B $\to$ K$^{(*)}\ell\ell$ decays, and the anomalous magnetic moment of the muon, can be explained by the existence of leptoquarks (LQs) with large couplings to third-generation quarks and masses at the TeV scale. The existence of these states can be probed at the LHC in high energy proton-proton collisions. A novel search is presented for pair production of LQs coupled to a top quark and a muon using data at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$, recorded by the CMS experiment. No deviation from the standard model prediction has been observed and scalar LQs decaying exclusively into t$\mu$ are excluded up to masses of 1420 GeV. The results of this search are combined with those from previous searches for LQ decays into t$\tau$ and b$\nu$, which excluded scalar LQs below masses of 900 and 1080 GeV. Vector LQs are excluded up to masses of 1190 GeV for all possible combinations of branching fractions to t$\mu$, t$\tau$ and b$\nu$. With this analysis, all relevant couplings of LQs with an electric charge of -1/3 to third-generation quarks are probed for the first time.

The study of global event shape variables can provide sensitive tests of predictions for multijet production in proton-proton collisions. This paper presents a study of several event shape variables calculated using jet four momenta in proton-proton collisions at a centre-of-mass energy of 13 TeV and uses data recorded with the CMS detector at the LHC corresponding to an integrated luminosity of 2.2 fb$^{-1}$. After correcting for detector effects, the resulting distributions are compared with several theoretical predictions. The agreement generally improves as the energy, represented by the average transverse momentum of the two leading jets, increases.

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 an exotic decay of the Higgs boson to a pair of light pseudoscalar bosons is performed for the first time in the final state with two b quarks and two $\tau$ leptons. The search is motivated in the context of models of physics beyond the standard model (SM), such as two Higgs doublet models extended with a complex scalar singlet (2HDM+S), which include the next-to-minimal supersymmetric SM (NMSSM). The results are based on a data set of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, accumulated by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV. Masses of the pseudoscalar boson between 15 and 60 GeV are probed, and no excess of events above the SM expectation is observed. Upper limits between 3 and 12% are set on the branching fraction $\mathcal{B}$(h $\to$ aa $\to$ 2$\tau$2b) assuming the SM production of the Higgs boson. Upper limits are also set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different 2HDM+S scenarios. Assuming the SM production cross section for the Higgs boson, the upper limit on this quantity is as low as 20% for a mass of the pseudoscalar of 40 GeV in the NMSSM.

A search for a Higgs boson decaying into a pair of electrons or muons and a photon is described. Higgs boson decays to a Z boson and a photon (H $\to$ Z$\gamma\to\ell\ell\gamma$, $\ell =$ e or $\mu$), or to two photons, one of which has an internal conversion into a muon pair (H $\to\gamma^{*}\gamma\to\mu\mu\gamma$) were considered. The analysis is performed using a data set recorded by the CMS experiment at the LHC from proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. No significant excess above the background prediction has been found. Limits are set on the cross section for a standard model Higgs boson decaying to opposite-sign electron or muon pairs and a photon. The observed limits on cross section times the corresponding branching fractions vary between 1.4 and 4.0 (6.1 and 11.4) times the standard model cross section for H $\to\gamma^{*}\gamma\to\mu\mu\gamma$ (H $\to$ Z$\gamma\to\ell\ell\gamma$) in the 120-130 GeV mass range of the $\ell\ell\gamma$ system. The H $\to\gamma^*\gamma\to\mu\mu\gamma$ and H $\to$ Z$\gamma\to\ell\ell\gamma$ analyses are combined for $m_\mathrm{H} =$ 125 GeV, obtaining an observed (expected) 95% confidence level upper limit of 3.9 (2.0) times the standard model cross section.