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 for long-lived particles decaying into jets is presented. Data were collected with the CMS detector at the LHC from proton-proton collisions at a center-of-mass energy of 13 TeV in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The search examines the distinctive topology of displaced tracks and secondary vertices. The selected events are found to be consistent with standard model predictions. For a simplified model in which long-lived neutral particles are pair produced and decay to two jets, pair production cross sections larger than 0.2 fb are excluded at 95% confidence level for a long-lived particle mass larger than 1000 GeV and proper decay lengths between 3 and 130 mm. Several supersymmetry models with gauge-mediated supersymmetry breaking or $R$-parity violation, where pair-produced long-lived gluinos or top squarks decay to several final-state topologies containing displaced jets, are also tested. For these models, in the mass ranges above 200 GeV, gluino masses up to 2300-2400 GeV and top squark masses up to 1350-1600 GeV are excluded for proper decay lengths approximately between 10 and 100 mm. These are the most restrictive limits to date on these models.

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.

A search for nonresonant excesses in the invariant mass spectra of electron and muon pairs is presented. The analysis is based on data from proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the CMS experiment in 2016, corresponding to a total integrated luminosity of 36 fb$^{-1}$. No significant deviation from the standard model is observed. Limits are set at 95% confidence level on energy scales for two general classes of nonresonant models. For a class of fermion contact interaction models, lower limits ranging from 20 to 32 TeV are set on the characteristic compositeness scale $\Lambda$. For the Arkani-Hamed, Dimopoulos, and Dvali model of large extra dimensions, the first results in the dilepton final state at 13 TeV are reported, and values of the ultraviolet cutoff parameter $\Lambda_\mathrm{T}$ below 6.9 TeV are excluded. A combination with recent CMS diphoton results improves this exclusion to $\Lambda_\mathrm{T}$ below 7.7 TeV, providing the most sensitive limits to date in nonhadronic final states.

For the first time, a search for the rare decay of the W boson to three charged pions has been performed. Proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 77.3 fb$^{-1}$, have been analyzed. No significant excess is observed above the background expectation. An upper limit of 1.01 $\times$ 10$^{-6}$ is set at 95% confidence level on the branching fraction of the W boson to three charged pions. This provides a strong motivation for theoretical calculations of this branching fraction.