Infrared and collinear safe event shape distributions and their mean values are determined in e+e- collisions at centre-of-mass energies between 45 and 202 GeV. A phenomenological analysis based on power correction models including hadron mass effects for both differential distributions and mean values is presented. Using power corrections, alpha_s is extracted from the mean values and shapes. In an alternative approach, renormalisation group invariance (RGI) is used as an explicit constraint, leading to a consistent description of mean values without the need for sizeable power corrections. The QCD beta-function is precisely measured using this approach. From the DELPHI data on Thrust, including data from low energy experiments, one finds beta_0 = 7.86 +/- 0.32 for the one loop coefficient of the beta-function or, assuming QCD, n_f = 4.75 +/- 0.44 for the number of active flavours. These values agree well with the QCD expectation of beta_0=7.67 and n_f=5. A direct measurement of the full logarithmic energy slope excludes light gluinos with a mass below 5 GeV.

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.

Measurements of the centrality and rapidity dependence of inclusive jet production in $\sqrt{s_\mathrm{NN}} = 5.02$ TeV proton--lead ($p$+Pb) collisions and the jet cross-section in $\sqrt{s} = 2.76$ TeV proton--proton collisions are presented. These quantities are measured in datasets corresponding to an integrated luminosity of 27.8 nb$^{-1}$ and 4.0 pb$^{-1}$, respectively, recorded with the ATLAS detector at the Large Hadron Collider in 2013. The $p$+Pb collision centrality was characterised using the total transverse energy measured in the pseudorapidity interval $-4.9 < \eta < -3.2$ in the direction of the lead beam. Results are presented for the double-differential per-collision yields as a function of jet rapidity and transverse momentum ($p_\mathrm{T}$) for minimum-bias and centrality-selected $p$+Pb collisions, and are compared to the jet rate from the geometric expectation. The total jet yield in minimum-bias events is slightly enhanced above the expectation in a $p_\mathrm{T}$-dependent manner but is consistent with the expectation within uncertainties. The ratios of jet spectra from different centrality selections show a strong modification of jet production at all $p_\mathrm{T}$ at forward rapidities and for large $p_\mathrm{T}$ at mid-rapidity, which manifests as a suppression of the jet yield in central events and an enhancement in peripheral events. These effects imply that the factorisation between hard and soft processes is violated at an unexpected level in proton-nucleus collisions. Furthermore, the modifications at forward rapidities are found to be a function of the total jet energy only, implying that the violations may have a simple dependence on the hard parton-parton kinematics.

Measurements of charged jet production as a function of centrality are presented for p-Pb collisions recorded at $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector. Centrality classes are determined via the energy deposit in neutron calorimeters at zero degree, close to the beam direction, to minimise dynamical biases of the selection. The corresponding number of participants or binary nucleon-nucleon collisions is determined based on the particle production in the Pb-going rapidity region. Jets have been reconstructed in the central rapidity region from charged particles with the anti-$k_{\rm T}$ algorithm for resolution parameters $R = 0.2$ and $R = 0.4$ in the transverse momentum range 20 to 120 GeV/$c$. The reconstructed jet momentum and yields have been corrected for detector effects and underlying-event background. In the five centrality bins considered, the charged jet production in p-Pb collisions is consistent with the production expected from binary scaling from pp collisions. The ratio of jet yields reconstructed with the two different resolution parameters is also independent of the centrality selection, demonstrating the absence of major modifications of the radial jet structure in the reported centrality classes.

The differential charged jet cross sections, jet fragmentation distributions, and jet shapes are measured in minimum bias proton-proton collisions at centre-of-mass energy $\sqrt{s}=7$ TeV using the ALICE detector at the LHC. Jets are reconstructed from charged particle momenta in the mid-rapidity region using the sequential recombination $k_{\rm T}$ and anti-$k_{\rm T}$ as well as the SISCone jet finding algorithms with several resolution parameters in the range $R=0.2$ to $0.6$. Differential jet production cross sections measured with the three jet finders are in agreement in the transverse momentum ($p_{\rm T}$) interval $20<p_{\rm T}^{\rm jet,ch}<100$ GeV/$c$. They are also consistent with prior measurements carried out at the LHC by the ATLAS collaboration. The jet charged particle multiplicity rises monotonically with increasing jet $p_{\rm T}$, in qualitative agreement with prior observations at lower energies. The transverse profiles of leading jets are investigated using radial momentum density distributions as well as distributions of the average radius containing 80% ($\langle R_{\rm 80} \rangle$) of the reconstructed jet $p_{\rm T}$. The fragmentation of leading jets with $R=0.4$ using scaled $p_{\rm T}$ spectra of the jet constituents is studied. The measurements are compared to model calculations from event generators (PYTHIA, PHOJET, HERWIG). The measured radial density distributions and $\langle R_{\rm 80} \rangle$ distributions are well described by the PYTHIA model (tune Perugia-2011). The fragmentation distributions are better described by HERWIG.

An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.

The dependence of inclusive jet production in proton-proton collisions with a center-of-mass energy of 13 TeV on the distance parameter $R$ of the anti-$k_\mathrm{T}$ algorithm is studied using data corresponding to integrated luminosities up to 35.9 fb$^{-1}$ collected by the CMS experiment in 2016. The ratios of the inclusive cross sections as functions of transverse momentum $p_\mathrm{T}$ and rapidity $y$, for $R$ in the range 0.1 to 1.2 to those using $R = $ 0.4 are presented in the region 84 $\lt$ $p_\mathrm{T}$ $\lt$ 1588 GeV and $|y|$ $\lt$ 2.0. The results are compared to calculations at leading and next-to-leading order in the strong coupling constant using different parton shower models. The variation of the ratio of cross sections with $R$ is well described by calculations including a parton shower model, but not by a leading-order quantum chromodynamics calculation including nonperturbative effects. The agreement between the data and the theoretical predictions for the ratios of cross sections is significantly improved when next-to-leading order calculations with nonperturbative effects are used.

Dijet cross sections are presented using photoproduction data obtained with the ZEUS detector during 1994. These measurements represent an extension of previous results, as the higher statistics allow cross sections to be measured at higher jet transverse energy (ETJ). Jets are identified in the hadronic final state using three different algorithms, and the cross sections compared to complete next-to-leading order QCD calculations. Agreement with these calculations is seen for the pseudorapidity dependence of the direct photon events with ETJ > 6 GeV and of the resolved photon events with ETJ > 11 GeV. Calculated cross sections for resolved photon processes with 6 GeV < ETJ < 11 GeV lie below the data.

Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above M Z with the DELPHI detector at LEP. From the event shapes, the strong coupling α s is extracted in O ( α s 2 ), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at M Z , the energy dependence (running) of α s is accessible. The logarithmic energy slope of the inverse strong coupling is measured to be d α −1 s d log (E cm ) =1.39±0.34( stat )±0.17( syst ) , in good agreement with the QCD expectation of 1.27.

The dynamics of isolated-photon plus one-, two- and three-jet production in $pp$ collisions at a centre-of-mass energy of 8 TeV are studied with the ATLAS detector at the LHC using a data set with an integrated luminosity of 20.2 fb$^{-1}$. Measurements of isolated-photon plus jets cross sections are presented as functions of the photon and jet transverse momenta. The cross sections as functions of the azimuthal angle between the photon and the jets, the azimuthal angle between the jets, the photon-jet invariant mass and the scattering angle in the photon-jet centre-of-mass system are presented. The pattern of QCD radiation around the photon and the leading jet is investigated by measuring jet production in an annular region centred on each object; enhancements are observed around the leading jet with respect to the photon in the directions towards the beams. The experimental measurements are compared to several different theoretical calculations, and overall a good description of the data is found.