Results are reported from a search for long-lived particles in proton-proton collisions at $\sqrt{s} =$ 13 TeV delivered by the CERN LHC and collected by the CMS experiment. The data sample, which was recorded during 2015 and 2016, corresponds to an integrated luminosity of 38.5 fb$^{-1}$. This search uses benchmark signal models in which long-lived particles are pair-produced and each decays into two or more quarks, leading to a signal with multiple jets and two displaced vertices composed of many tracks. No events with two well-separated high-track-multiplicity vertices are observed. Upper limits are placed on models of $R$-parity violating supersymmetry in which the long-lived particles are neutralinos or gluinos decaying solely into multijet final states or top squarks decaying solely into dijet final states. For neutralino, gluino, or top squark masses between 800 and 2600 GeV and mean proper decay lengths between 1 and 40 mm, the analysis excludes cross sections above 0.3 fb at 95% confidence level. Gluino and top squark masses are excluded below 2200 and 1400 GeV, respectively, for mean proper decay lengths between 0.6 and 80 mm. A method is provided for extending the results to other models with pair-produced long-lived particles.

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.

Measurements of differential top quark pair $\mathrm{t\overline{t}}$ cross sections using events produced in proton-proton collisions at a centre-of-mass energy of 13 TeV containing two oppositely charged leptons are presented. The data were recorded by the CMS experiment at the CERN LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The differential cross sections are presented as functions of kinematic observables of the top quarks and their decay products, the $\mathrm{t\overline{t}}$ system, and the total number of jets in the event. The differential cross sections are defined both with particle-level objects in a fiducial phase space close to that of the detector acceptance and with parton-level top quarks in the full phase space. All results are compared with standard model predictions from Monte Carlo simulations with next-to-leading-order (NLO) accuracy in quantum chromodynamics (QCD) at matrix-element level interfaced to parton-shower simulations. Where possible, parton-level results are compared to calculations with beyond-NLO precision in QCD. Significant disagreement is observed between data and all predictions for several observables. The measurements are used to constrain the top quark chromomagnetic dipole moment in an effective field theory framework at NLO in QCD and to extract $\mathrm{t\overline{t}}$ and leptonic charge asymmetries.

Measurements of the differential jet cross section are presented as a function of jet mass in dijet events, in bins of jet transverse momentum, with and without a jet grooming algorithm. The data have been recorded by the CMS Collaboration in proton-proton collisions at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 2.3 fb$^{-1}$. The absolute cross sections show slightly different jet transverse momentum spectra in data and Monte Carlo event generators for the settings used. Removing this transverse momentum dependence, the normalized cross section for ungroomed jets is consistent with the prediction from Monte Carlo event generators for masses below 30% of the transverse momentum. The normalized cross section for groomed jets is measured with higher precision than the ungroomed cross section. Semi-analytical calculations of the jet mass beyond leading logarithmic accuracy are compared to data, as well as predictions at leading order and next-to-leading order, which include parton showering and hadronization. Overall, in the normalized cross section, the theoretical predictions agree with the measured cross sections within the uncertainties for masses from 10 to 30% of the jet transverse momentum.

Normalized differential cross sections for top quark pair production are measured in the dilepton (e$^+$e$^-$, $\mu^+\mu^-$, and $\mu^\mp$e$^\pm$) decay channels in proton-proton collisions at a center-of-mass energy of 13 TeV. The measurements are performed with data corresponding to an integrated luminosity of 2.1 fb$^{-1}$ using the CMS detector at the LHC. The cross sections are measured differentially as a function of the kinematic properties of the leptons, jets from bottom quark hadronization, top quarks, and top quark pairs at the particle and parton levels. The results are compared to several Monte Carlo generators that implement calculations up to next-to-leading order in perturbative quantum chromodynamics interfaced with parton showering, and also to fixed-order theoretical calculations of top quark pair production up to next-to-next-to-leading order.

A search is presented for physics beyond the standard model, based on measurements of dijet angular distributions in proton-proton collisions at $\sqrt{s}=$ 13 TeV. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 35.9 fb$^{-1}$. The observed distributions are found to be in agreement with predictions from perturbative quantum chromodynamics that include electroweak corrections. Constraints are placed on models containing quark contact interactions, extra spatial dimensions, quantum black holes, or dark matter using the detector-level distributions. In a benchmark model where only left-handed quarks participate, contact interactions are excluded at the 95% confidence level up to a scale of 12.8 or 17.5 TeV, for destructive or constructive interference, respectively. The most stringent lower limits to date are set on the ultraviolet cutoff in the Arkani-Hamed-Dimopoulos-Dvali model of extra dimensions. In the Giudice-Rattazzi-Wells convention, the cutoff scale is excluded up to 10.1 TeV. The production of quantum black holes is excluded for masses below 5.9 and 8.2 TeV, depending on the model. For the first time, lower limits between 2.0 and 4.6 TeV are set on the mass of a dark matter mediator for (axial-)vector mediators, for the universal quark coupling $g_\mathrm{q}\geq$ 1.

Jet charge is an estimator of the electric charge of a quark, antiquark, or gluon initiating a jet. It is based on the momentum-weighted sum of the electric charges of the jet constituents. Measurements of three charge observables of the leading jet in transverse momentum pT are performed with dijet events. The analysis is carried out with data collected by the CMS experiment at the CERN LHC in proton-proton collisions at sqrt(s) = 8 TeV corresponding to an integrated luminosity of 19.7 inverse femtobarns. The results are presented as a function of the pT of the leading jet and compared to predictions from leading- and next-to-leading-order event generators combined with parton showers. Measured jet charge distributions, unfolded for detector effects, are reported, which expand on previous measurements of the jet charge average and standard deviation in pp collisions.

A search is presented for the decays of heavy exotic long-lived particles (LLPs) that are produced in proton-proton collisions at a center-of-mass energy of 13 TeV at the CERN LHC and come to rest in the CMS detector. Their decays would be visible during periods of time well separated from proton-proton collisions. Two decay scenarios of stopped LLPs are explored: a hadronic decay detected in the calorimeter and a decay into muons detected in the muon system. The calorimeter (muon) search covers a period of sensitivity totaling 721 (744) hours in 38.6 (39.0) fb$^{-1}$ of data collected by the CMS detector in 2015 and 2016. The results are interpreted in several scenarios that predict LLPs. Production cross section limits are set as a function of the mean proper lifetime and the mass of the LLPs, for lifetimes between 100 ns and 10 days. These are the most stringent limits to date on the mass of hadronically decaying stopped LLPs, and this is the first search at the LHC for stopped LLPs that decay to muons.

The production of a Z boson, decaying to two charged leptons, in association with jets in proton-proton collisions at a centre-of-mass energy of 13 TeV is measured. Data recorded with the CMS detector at the LHC are used that correspond to an integrated luminosity of 2.19 fb$^{-1}$. The cross section is measured as a function of the jet multiplicity and its dependence on the transverse momentum of the Z boson, the jet kinematic variables (transverse momentum and rapidity), the scalar sum of the jet momenta, which quantifies the hadronic activity, and the balance in transverse momentum between the reconstructed jet recoil and the Z boson. The measurements are compared with predictions from four different calculations. The first two merge matrix elements with different parton multiplicities in the final state and parton showering, one of which includes one-loop corrections. The third is a fixed-order calculation with next-to-next-to-leading order accuracy for the process with a Z boson and one parton in the final state. The fourth combines the fully differential next-to-next-to-leading order calculation with next-to-next-to-leading logarithm resummation and parton showering.

Results are reported for the ${\rm B_s^0}\to\mu^+\mu^-$ branching fraction and effective lifetime and from a search for the decay ${\rm B^0}\to\mu^+\mu^-$. The analysis uses a data sample of proton-proton collisions accumulated by the CMS experiment in 2011, 2012, and 2016, with center-of-mass energies (integrated luminosities) of 7 TeV (5 fb$^{-1}$), 8 TeV (20 fb$^{-1}$), and 13 TeV (36 fb$^{-1}$). The branching fractions are determined by measuring efficiency-corrected event yields relative to ${\rm B^+}\to{\rm J}/\psi {\rm K^+}$ decays (with ${\rm J}/\psi\to\mu^+\mu^-$), which results in the cancellation of many of the systematic uncertainties. The decay ${\rm B_s^0}\to\mu^+\mu^-$ is observed with a branching fraction of ${\cal B}({\rm B_s^0}\to\mu^+\mu^-) = {[2.9^{+0.7}_{-0.6}\,(\text{exp})\pm{0.2}\,(\text{frag})]\times10^{-9}}$, where frag refers to the uncertainty in the ratio $f_s/f_u$ of the ${\rm B_s^0}$ and the ${\rm B^+}$ fragmentation functions, corresponding to a significance of 5.6 standard deviations. No significant excess is observed for the decay ${\rm B^0}\to\mu^+\mu^-$, and the upper limit ${\cal B}({\rm B^0}\to\mu^+\mu^-) < {3.6\times10^{-10}}$ is obtained at $95\%$ confidence level. These measured branching fractions are consistent with standard model predictions, and they supersede previous results from CMS based on the 2011 and 2012 data only. Finally, the ${\rm B_s^0}\to\mu^+\mu^-$ effective lifetime is measured, for the first time in CMS, and is found to be $\tau_{\mu^+\mu^-} = {1.70^{+0.61}_{-0.44}}$ ps.