This Letter describes a search for Higgs boson pair production using the combined results from four final states: bb$\gamma\gamma$, bb$\tau\tau$, bbbb, and bbVV, where V represents a W or Z boson. The search is performed using data collected in 2016 by the CMS experiment from LHC proton-proton collisions at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Limits are set on the Higgs boson pair production cross section. A 95% confidence level observed (expected) upper limit on the nonresonant production cross section is set at 22.2 (12.8) times the standard model value. A search for narrow resonances decaying to Higgs boson pairs is also performed in the mass range 250-3000 GeV. No evidence for a signal is observed, and upper limits are set on the resonance production cross section.

Results are presented from a search for new decaying massive particles whose presence is inferred from an imbalance in transverse momentum and which are produced in association with a single top quark that decays into a bottom quark and two light quarks. The measurement is performed using 19.7 inverse femtobarns of data from proton-proton collisions at a center-of-mass energy of 8 TeV, collected with the CMS detector at the CERN LHC. No deviations from the standard model predictions are observed and lower limits are set on the masses of new invisible bosons. In particular, scalar and vector particles, with masses below 330 and 650 GeV, respectively, are excluded at 95% confidence level, thus substantially extending a previous limit published by the CDF Collaboration.

The elliptic azimuthal anisotropy coefficient ($v_2$) is measured for charm (D$^0$) and strange (K$_\mathrm{S}^0$, $\Lambda$, $\Xi^-$, and $\Omega^-$) hadrons, using a data sample of pPb collisions collected by the CMS experiment, at a nucleon-nucleon center-of-mass energy $\sqrt{s_{_\mathrm{NN}}} =$ 8.16 TeV. A significant positive $v_2$ signal from long-range azimuthal correlations is observed for all particle species in high-multiplicity pPb collisions. The measurement represents the first observation of possible long-range collectivity for open heavy flavor hadrons in small systems. The results suggest that charm quarks have a smaller $v_2$ than the lighter quarks, probably reflecting a weaker collective behavior. This effect is not seen in the larger PbPb collision system at $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 TeV, also presented.

Data from heavy ion collisions suggest that the evolution of a parton shower is modified by interactions with the color charges in the dense partonic medium created in these collisions, but it is not known where in the shower evolution the modifications occur. The momentum ratio of the two leading partons, resolved as subjets, provides information about the parton shower evolution. This substructure observable, known as the splitting function, reflects the process of a parton splitting into two other partons and has been measured for jets with transverse momentum between 140 and 500 GeV, in pp and PbPb collisions at a center-of-mass energy of 5.02 GeV per nucleon pair. In central PbPb collisions, the splitting function indicates a more unbalanced momentum ratio, compared to peripheral PbPb and pp collisions. The measurements are compared to various predictions from event generators and analytical calculations.

The polarization of $\tau$ leptons is measured using leptonic and hadronic $\tau$ lepton decays in Z $\to$$\tau^+\tau^-$ events in proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb$^{-1}$. The measured $\tau^-$ polarization at the Z boson mass pole is $\mathcal{P}_{\tau}$(Z) = $-$0.144 $\pm$ 0.006 (stat) $\pm$ 0.014 (syst) = $-$0.144 $\pm$ 0.015, in good agreement with the measurement of the $\tau$ lepton asymmetry parameter of $A_{\tau}$ = 0.1439 $\pm$ 0.0043 = $-\mathcal{P}_{\tau}$(Z) at LEP. The $\tau$ polarization depends on the ratio of the vector to axial-vector couplings of the $\tau$ leptons in the neutral current expression, and thus on the effective weak mixing angle $\sin^{2}\theta_\mathrm{W}^{\text{eff}}$, independently of the Z boson production mechanism. The obtained value $\sin^{2}\theta_\mathrm{W}^{\text{eff}}$ = 0.2319 $\pm$ 0.0008 (stat) $\pm$ 0.0018 (syst) = 0.2319 $\pm$ 0.0019 is in good agreement with measurements at e$^+$e$^-$ colliders.

The first measurements of the Fourier coefficients ($V_{n\Delta}$) of the azimuthal distributions of charged hadrons emitted from photon-proton ($\gamma$p) interactions at the LHC are presented. The data are extracted from 68.8 nb$^{-1}$ of ultra-peripheral proton-lead (pPb) collisions at $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV using the CMS detector. The high energy lead ions produce a flux of photons that can interact with the oncoming proton. This $\gamma$p system provides a set of unique initial conditions with multiplicity lower than in photon-lead collisions but comparable to recent electron-positron and electron-proton data. The $V_{n\Delta}$ coefficients are presented in ranges of event multiplicity and transverse momentum ($p_\mathrm{T}$) and are compared to corresponding hadronic minimum bias pPb results. For a given multiplicity range, the mean $p_\mathrm{T}$ of charged particles is smaller in $\gamma$p than in pPb collisions. For both the $\gamma$p and pPb samples, $V_{1\Delta}$ is negative, $V_{2\Delta}$ is positive, and $V_{3\Delta}$ consistent with 0. For each multiplicity and $p_\mathrm{T}$ range, $V_{2\Delta}$ is larger for $\gamma$p events. The $\gamma$p data are consistent with model predictions that have no collective effects.

The central exclusive production of charged-hadron pairs in pp collisions at a centre-of-mass energy of 13\TeV is examined, based on data collected in a special high-$\beta^*$ run of the LHC. The nonresonant continuum processes are studied with the invariant mass of the centrally produced two-pion system in the resonance-free region, $m_{\pi^+\pi^-}$$\lt$ 0.7 GeV or $m_{\pi^+\pi^-}$$\gt$ 1.8 GeV. Differential cross sections as functions of the azimuthal angle between the surviving protons, squared exchanged four-momenta, and $m_{\pi^+\pi^-}$ are measured in a wide region of scattered proton transverse momenta, between 0.2 and 0.8 GeV, and for pion rapidities $\lvert y\rvert$$\lt$ 2. A rich structure of interactions related to double-pomeron exchange is observed. A parabolic minimum in the distribution of the two-proton azimuthal angle is observed for the first time. It can be interpreted as an effect of additional pomeron exchanges between the protons from the interference between the bare and the rescattered amplitudes. After model tuning, various physical quantities are determined that are related to the pomeron cross section, proton-pomeron and meson-pomeron form factors, pomeron trajectory and intercept, and coefficients of diffractive eigenstates of the proton.

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 search for the central exclusive production of top quark-antiquark pairs ($\mathrm{t\bar{t}}$) is performed for the first time using proton-tagged events in proton-proton collisions at the LHC at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 29.4 fb$^{-1}$. The $\mathrm{t\bar{t}}$ decay products are reconstructed using the central CMS detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer. An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb is set at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and 20%.

A search for narrow resonances in the dijet mass spectrum is performed using data corresponding to an integrated luminosity of 2.9 inverse pb collected by the CMS experiment at the LHC. Upper limits at the 95% confidence level (CL) are presented on the product of the resonance cross section, branching fraction into dijets, and acceptance, separately for decays into quark-quark, quark-gluon, or gluon-gluon pairs. The data exclude new particles predicted in the following models at the 95% CL: string resonances, with mass less than 2.50 TeV, excited quarks, with mass less than 1.58 TeV, and axigluons, colorons, and E_6 diquarks, in specific mass intervals. This extends previously published limits on these models.