The double differential cross sections of the Drell-Yan lepton pair ($\ell^+\ell^-$, dielectron or dimuon) production are measured as functions of the invariant mass $m_{\ell\ell}$, transverse momentum $p_\mathrm{T}(\ell\ell)$, and $\phi^*_\eta$. The $\phi^*_\eta$ observable, derived from angular measurements of the leptons and highly correlated with $p_\mathrm{T}(\ell\ell)$, is used to probe the low-$p_\mathrm{T}(\ell\ell)$ region in a complementary way. Dilepton masses up to 1 TeV are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various $m_{\ell\ell}$ ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3 fb$^{-1}$ of proton-proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13 TeV. Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

Double-parton scattering is investigated using events with a Z boson and jets. The Z boson is reconstructed using only the dimuon channel. The measurements are performed with proton-proton collision data recorded by the CMS experiment at the LHC at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$ collected in the year 2016. Differential cross sections of Z + $\geq$ 1 jet and Z + $\geq$ 2 jets are measured with transverse momentum of the jets above 20 GeV and pseudorapidity $|\eta|$$\lt$ 2.4. Several distributions with sensitivity to double-parton scattering effects are measured as functions of the angle and the transverse momentum imbalance between the Z boson and the jets. The measured distributions are compared with predictions from several event generators with different hadronization models and different parameter settings for multiparton interactions. The measured distributions show a dependence on the hadronization and multiparton interaction simulation parameters, and are important input for future improvements of the simulations.

Differential cross sections for the Drell-Yan process, including Z boson production, using the dimuon decay channel are measured in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of 8.16 TeV. A data sample recorded with the CMS detector at the LHC is used, corresponding to an integrated luminosity of 173 nb$^{-1}$. The differential cross section as a function of the dimuon mass is measured in the range 15-600 GeV, for the first time in proton-nucleus collisions. It is also reported as a function of dimuon rapidity over the mass ranges 15-60 GeV and 60-120 GeV, and ratios for the p-going over the Pb-going beam directions are built. In both mass ranges, the differential cross sections as functions of the dimuon transverse momentum $p_\mathrm{T}$ and of a geometric variable $\phi^*$ are measured, where $\phi^*$ highly correlates with $p_\mathrm{T}$ but is determined with higher precision. In the Z mass region, the rapidity dependence of the data indicate a modification of the distribution of partons within a lead nucleus as compared to the proton case. The data are more precise than predictions based upon current models of parton distributions.

The normalized differential cross section for top quark pair (tt-bar) production is measured in pp collisions at a centre-of-mass energy of 8 TeV at the CERN LHC using the CMS detector in data corresponding to an integrated luminosity of 19.7 inverse femtobarns. The measurements are performed in the lepton + jets (e/mu + jets) and in the dilepton (e+e-, mu+mu-, and e+-mu-+) decay channels. The tt-bar cross section is measured as a function of the kinematic properties of the charged leptons, the jets associated to b quarks, the top quarks, and the tt-bar system. The data are compared with several predictions from perturbative quantum chromodynamics up to approximate next-to-next-to-leading-order precision. No significant deviations are observed relative to the standard model predictions.

The per-event yield of the highest transverse momentum charged particle and charged-particle jet, integrated above a given pt(min) threshold starting at pt(min) = 0.8 and 1 GeV, respectively, is studied in pp collisions at sqrt(s) = 8 TeV. The particles and the jets are measured in the pseudorapidity ranges abs(eta) < 2.4 and 1.9, respectively. The data are sensitive to the momentum scale at which parton densities saturate in the proton, to multiple partonic interactions, and to other key aspects of the transition between the soft and hard QCD regimes in hadronic collisions.

A measurement of the differential cross sections for a W boson produced in association with jets in the muon decay channel is presented. The measurement is based on 13 TeV proton-proton collision data corresponding to an integrated luminosity of 2.2 inverse femtobarns, recorded by the CMS detector at the LHC. The cross sections are reported as functions of jet multiplicity, jet transverse momentum pT, jet rapidity, the scalar pT sum of the jets, and angular correlations between the muon and the jet for different jet multiplicities. The measured cross sections are in agreement with predictions that include multileg leading-order (LO) and next-to-LO matrix element calculations interfaced with parton showers, as well as a next-to-next-to-LO calculation for the W boson and one jet production.

Measurements of the differential cross sections for the production of exactly four jets in proton-proton collisions are presented as a function of the transverse momentum pt and pseudorapidity eta, together with the correlations in azimuthal angle and the pt balance among the jets. The data sample was collected in 2010 at a center-of-mass energy of 7 TeV with the CMS detector at the LHC, with an integrated luminosity of 36 inverse picobarns. The cross section for a final state with a pair of hard jets with pt > 50 GeV and another pair with pt > 20 GeV within abs(eta) < 4.7 is measured to be sigma = 330 +- 5 (stat.) +- 45 (syst.) nb. It is found that fixed-order matrix element calculations including parton showers describe the measured differential cross sections in some regions of phase space only, and that adding contributions from double parton scattering brings the Monte Carlo predictions closer to the data.

Measurements of differential cross sections are presented for the production of a Z boson and at least one hadronic jet in proton-proton collisions at sqrt(s) = 7 TeV, recorded by the CMS detector, using a data sample corresponding to an integrated luminosity of 4.9 inverse femtobarns. The jet multiplicity distribution is measured for up to six jets. The differential cross sections are measured as a function of jet transverse momentum and pseudorapidity for the four highest transverse momentum jets. The distribution of the scalar sum of jet transverse momenta is also measured as a function of the jet multiplicity. The measurements are compared with theoretical predictions at leading and next-to-leading order in perturbative QCD.

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pt) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 inverse femtobarns. The measured cross sections are compared to predictions from Monte Carlo generators, MADGRAPH + PYTHIA and SHERPA, and to next-to-leading-order calculations from BLACKHAT + SHERPA. The differential cross sections are found to be in agreement with the predictions, apart from the pt distributions of the leading jets at high pt values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.

Characteristics of multi-particle production in proton-proton collisions at $\sqrt{s}$=7 TeV are studied as a function of the charged-particle multiplicity, $N_{ch}$. The produced particles are separated into two classes: those belonging to jets and those belonging to the underlying event. Charged particles are measured with pseudorapidity |η|<2.4 and transverse momentum $p_T$ > 0.25 GeV/c. Jets are reconstructed from charged-particles only and required to have $p_T$ > 5 GeV/c. The distributions of jet $p_T$, average $p_T$ of charged particles belonging to the underlying event or to jets, jet rates, and jet shapes are presented as functions of $N_{ch}$ and compared to the predictions of the PYTHIA and HERWIG event generators. Predictions without multi-parton interactions fail completely to describe the $N_{ch}$-dependence observed in the data. For increasing $N_{ch}$, PYTHIA systematically predicts higher jet rates and harder $p_T$ spectra than seen in the data, whereas HERWIG shows the opposite trends. At the highest multiplicity, the data–model agreement is worse for most observables, indicating the need for further tuning and/or new model ingredients.