We present the first measurement of the inclusive three-jet differential cross section as a function of the invariant mass of the three jets with the largest transverse momenta in an event in p anti-p collisions at sqrt(s) = 1.96 TeV. The measurement is made in different rapidity regions and for different jet transverse momentum requirements and is based on a data set corresponding to an integrated luminosity of 0.7 fb^{-1} collected with the D0 detector at the Fermilab Tevatron Collider. The results are used to test the three-jet matrix elements in perturbative QCD calculations at next-to-leading order in the strong coupling constant. The data allow discrimination between parametrizations of the parton distribution functions of the proton.

A measurement of the decorrelation of azimuthal angles between the two jets with the largest transverse momenta is presented for seven regions of leading jet transverse momentum up to 2.2 TeV. The analysis is based on the proton-proton collision data collected with the CMS experiment at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 19.7 inverse femtobarns. The dijet azimuthal decorrelation is caused by the radiation of additional jets and probes the dynamics of multijet production. The results are compared to fixed-order predictions of perturbative quantum chromodynamics (QCD), and to simulations using Monte Carlo event generators that include parton showers, hadronization, and multiparton interactions. Event generators with only two outgoing high transverse momentum partons fail to describe the measurement, even when supplemented with next-to-leading-order QCD corrections and parton showers. Much better agreement is achieved when at least three outgoing partons are complemented through either next-to-leading-order predictions or parton showers. This observation emphasizes the need to improve predictions for multijet production.

Measurements are presented of the cross section for the production of at least four jets, of which at least two originate from b quarks, in proton-proton collisions. Data collected with the CMS detector at the LHC at a center-of-mass energy of 7 TeV are used, corresponding to an integrated luminosity of 3 inverse picobarns. The cross section is measured as a function of the jet transverse momentum for pt > 20 GeV, and of the jet pseudorapidity for abs(eta) < 2.4 (b jets), 4.7 (untagged jets). The correlations in azimuthal angle and pt between the jets are also studied. The inclusive cross section is measured to be sigma(pp to 2 b + 2 j + X) = 69 +/- 3 (stat) +/- 24 (syst) nb. The eta and pt distributions of the four jets and the correlations between them are well reproduced by event generators that combine perturbative QCD calculations at next-to-leading-order accuracy with contributions from parton showers and multiparton interactions.

A measurement of the double-differential inclusive jet cross section as a function of jet transverse momentum pT and absolute jet rapidity |y| is presented. The analysis is based on proton-proton collisions collected by the CMS experiment at the LHC at a centre-of-mass energy of 13 TeV. The data samples correspond to integrated luminosities of 71 and 44 inverse picobarns for |y| < 3 and 3.2 < |y| < 4.7, respectively. Jets are reconstructed with the anti-kt clustering algorithm for two jet sizes, R, of 0.7 and 0.4, in a phase space region covering jet pT up to 2 TeV and jet rapidity up to |y| = 4.7. Predictions of perturbative quantum chromodynamics at next-to-leading order precision, complemented with electroweak and nonperturbative corrections, are used to compute the absolute scale and the shape of the inclusive jet cross section. The cross section difference in R, when going to a smaller jet size of 0.4, is best described by Monte Carlo event generators with next-to-leading order predictions matched to parton showering, hadronisation, and multiparton interactions. In the phase space accessible with the new data, this measurement provides a first indication that jet physics is as well understood at sqrt(s) = 13 TeV as at smaller centre-of-mass energies.

Differential cross sections for a W boson produced in association with jets are measured in a data sample of proton-proton collisions at a center-of-mass energy of 8 TeV recorded with the CMS detector and corresponding to an integrated luminosity of 19.6 inverse femtobarns. The W bosons are identified through their decay mode W to mu nu. The cross sections are reported as functions of jet multiplicity, transverse momenta, and the scalar sum of jet transverse momenta (HT) for different jet multiplicities. Distributions of the angular correlations between the jets and the muon are examined, as well as the average number of jets as a function of HT and as a function of angular variables. The measured differential cross sections are compared with tree-level and higher-order recent event generators, as well as next-to-leading-order and next-to-next-to-leading-order theoretical predictions. The agreement of the generators with the measurements builds confidence in their use for the simulation of W+jets background processes in searches for new physics at the LHC.

Multijet events at large transverse momentum ($p_\mathrm{T}$) are measured at $\sqrt{s}$ = 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with $p_\mathrm{T}$$>$ 50 GeV that are produced in association with a high-$p_\mathrm{T}$ dijet system is measured in various ranges of the $p_\mathrm{T}$ of the jet with the highest transverse momentum and as a function of the azimuthal angle difference $\Delta\phi_{1,2}$ between the two highest $p_\mathrm{T}$ jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $p_\mathrm{T}$ jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

Cross sections for the production of a Z boson in association with jets in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 8 TeV are measured using a data sample collected by the CMS experiment at the LHC corresponding to 19.6 inverse femtobarns. Differential cross sections are presented as functions of up to three observables that describe the jet kinematics and the jet activity. Correlations between the azimuthal directions and the rapidities of the jets and the Z boson are studied in detail. The predictions of a number of multileg generators with leading or next-to-leading order accuracy are compared with the measurements. The comparison shows the importance of including multi-parton contributions in the matrix elements and the improvement in the predictions when next-to-leading order terms are included.

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.

Azimuthal correlations between the two jets with the largest transverse momenta $ {p_{\mathrm{T}}} $ in inclusive 2-, 3-, and 4-jet events are presented for several regions of the leading jet $ {p_{\mathrm{T}}} $ up to 4 TeV. For 3- and 4-jet scenarios, measurements of the minimum azimuthal angles between any two of the three or four leading $ {p_{\mathrm{T}}} $ jets are also presented. The analysis is based on data from proton-proton collisions collected by the CMS Collaboration at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Calculations based on leading-order matrix elements supplemented with parton showering and hadronization do not fully describe the data, so next-to-leading-order calculations matched with parton shower and hadronization models are needed to better describe the measured distributions. Furthermore, we show that azimuthal jet correlations are sensitive to details of the parton showering, hadronization, and multiparton interactions. A next-to-leading-order calculation matched with parton showers in the MC@NLO method, as implemented in HERWIG 7, gives a better overall description of the measurements than the POWHEG method.

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.