The shapes of jets with transverse energies, E_T(jet), up to 45 GeV produced in neutral- and charged-current deep inelastic e+p scattering (DIS) at Q**2 > 100 GeV**2 have been measured with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the eta-phi plane with a cone radius of one unit. The jets become narrower as E_T(jet) increases. The jet shapes in neutral- and charged-current DIS are found to be very similar. The jets in neutral-current DIS are narrower than those in resolved processes in photoproduction and closer to those in direct-photon processes for the same ranges in E_T(jet) and jet pseudorapidity. The jet shapes in DIS are observed to be similar to those in e+e- interactions and narrower than those in pbarp collisions for comparable E_T(jet). Since the jets in e+e- interactions and e+p DIS are predominantly quark initiated in both cases, the similarity in the jet shapes indicates that the pattern of QCD radiation within a quark jet is to a large extent independent of the hard scattering process in these reactions.

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.

The cross section for dijet photoproduction at high transverse energies is presented as a function of the transverse energies and the pseudorapidities of the jets. The measurement is performed using a sample of ep-interactions corresponding to an integrated luminosity of 6.3 pb^(-1), recorded by the ZEUS detector.Jets are defined by applying a k_T-clustering algorithm to the hadrons observed in the final state. The measured cross sections are compared to next-to-leading order QCD calculations. In a kinematic regime where theoretical uncertainties are expected to be small, the measured cross sections are higher than these calculations.

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.

We have studied hadronic events produced at LEP at centre-of-mass energies of 130 and 136 GeV. Distributions of event shape observables, jet rates, momentum spectra and multiplicities are presented and compared to the predictions of several Monte Carlo models and analytic QCD calculations. From fits of event shape and jet rate distributions to\({\mathcal{O}}(\alpha _s^2 ) + NLLA\) QCD calculations, we determineαs(133 GeV)=0.110±0.005(stat.)±0.009(syst.). We measure the mean charged particle multiplicity 〈nch〉=23.40±0.45(stat.) ±0.47(syst.) and the position ζ0 of the peak in the ζp = ln(1/xp) distribution ζ0=3.94±0.05(stat.)±0.11(syst.). These results are compared to lower energy data and to analytic QCD or Monte Carlo predictions for their energy evolution.

Inclusive charged particle and event shape distributions are measured using 321 hadronic events collected with the DELPHI experiment at LEP at effective centre of mass energies of 130 to 136 GeV. These distributions are presented and compared to data at lower energies, in particular to the precise Z data. Fragmentation models describe the observed changes of the distributions well. The energy dependence of the means of the event shape variables can also be described using second order QCD plus power terms. A method independent of fragmentation model corrections is used to determine αs from the energy dependence of the mean thrust and heavy jet mass. It is measured to be: $$←pha _s(133 {⤪ GeV})={0.116}pm {0.007}_{exp-0.004theo}^{+0.005}$$ from the high energy data.

Inclusive dijet and trijet production in deep inelastic $ep$ scattering has been measured for $10&lt;Q^2&lt;100$ GeV$^2$ and low Bjorken $x$, $10^{-4}&lt;x_{\rm Bj}&lt;10^{-2}$. The data were taken at the HERA $ep$ collider with centre-of-mass energy $\sqrt{s} = 318 \gev$ using the ZEUS detector and correspond to an integrated luminosity of $82 {\rm pb}^{-1}$. Jets were identified in the hadronic centre-of-mass (HCM) frame using the $k_{T}$ cluster algorithm in the longitudinally invariant inclusive mode. Measurements of dijet and trijet differential cross sections are presented as functions of $Q^2$, $x_{\rm Bj}$, jet transverse energy, and jet pseudorapidity. As a further examination of low-$x_{\rm Bj}$ dynamics, multi-differential cross sections as functions of the jet correlations in transverse momenta, azimuthal angles, and pseudorapidity are also presented. Calculations at $\mathcal{O}(\alpha_{s}^3)$ generally describe the trijet data well and improve the description of the dijet data compared to the calculation at $\mathcal{O}(\alpha_{s}^2)$.

We have studied hadronic events produced at LEP at a centre-of-mass energy of 161 GeV. We present distributions of event shape variables, jet rates, charged particle momentum spectra and multiplicities. We determine the strong coupling strength to be αs(161 GeV) = 0.101±0.005(stat.)±0.007(syst.), the mean charged particle multiplicity to be 〈nch〉(161 GeV) = 24.46 ± 0.45(stat.) ± 0.44(syst.) and the position of the peak in the ξp = ln(1/xp) distribution to be ξ0(161 GeV) = 4.00 ±0.03(stat.)±0.04(syst.). These results are compared to data taken at lower centre-of-mass energies and to analytic QCD or Monte Carlo predictions. Our measured value of αs(161 GeV) is consistent with other measurements of αs. Within the current statistical and systematic uncertainties, the PYTHIA, HERWIG and ARIADNE QCD Monte Carlo models and analytic calculations are in overall agreement with our measurements. The COJETS QCD Monte Carlo is in general agreement with the data for momentum weighted distributions like Thrust, but predicts a significantly larger charged particle multiplicity than is observed experimentally.

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.

Jet substructure and differential cross sections for jets produced in the photoproduction and deep inelastic ep scattering regimes have been measured with the ZEUS detector at HERA using an integrated luminosity of 82.2 pb-1. The substructure of jets has been studied in terms of the jet shape and subjet multiplicity for jets with transverse energies Et(jet) > 17 GeV. The data are well described by the QCD calculations. The jet shape and subjet multiplicity are used to tag gluon- and quark-initiated jets. Jet cross sections as functions of Et(jet), jet pseudorapidity, the jet-jet scattering angle, dijet invariant mass and the fraction of the photon energy carried by the dijet system are presented for gluon- and quark-tagged jets. The data exhibit the behaviour expected from the underlying parton dynamics. A value of alphas(Mz) of alphas(Mz) = 0.1176 +-0.0009(stat.) -0.0026 +0.0009 (exp.) -0.0072 +0.0091 (th.) was extracted from the measurements of jet shapes in deep inelastic scattering.