Differential inclusive-jet cross sections have been measured for different jet radii in neutral current deep inelastic ep scattering for boson virtualities Q^2 > 125 GeV^2 with the ZEUS detector at HERA using an integrated luminosity of 81.7 pb^-1. Jets were identified in the Breit frame using the k_T cluster algorithm in the longitudinally inclusive mode for different values of the jet radius R. Differential cross sections are presented as functions of Q^2 and the jet transverse energy, E_T,B^jet. The dependence on R of the inclusive-jet cross section has been measured for Q^2 > 125 and 500 GeV^2 and found to be linear with R in the range studied. Next-to-leading-order QCD calculations give a good description of the measurements for 0.5 <= R <= 1. A value of alpha_s(M_Z) has been extracted from the measurements of the inclusive-jet cross-section dsigma/dQ^2 with R=1 for Q^2 > 500 GeV^2: alpha_s(M_Z) = 0.1207 +- 0.0014 (stat.) -0.0033 +0.0035 (exp.) -0.0023 +0.0022 (th.). The variation of alpha_s with E_T,B^jet is in good agreement with the running of alpha_s as predicted by QCD.
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Jet production in deep inelastic scattering for $120<Q~2<3600$GeV$~2$ has been studied using data from an integrated luminosity of 3.2pb$~{-1}$ collected with the ZEUS detector at HERA. Jets are identified with the JADE algorithm. A cut on the angular distribution of parton emission in the $\gamma~*$-parton centre-of-mass system minimises the experimental and theoretical uncertainties in the determination of the jet rates. The jet rates, when compared to ${\cal O}$($\alpha_{s}$~2$) perturbative QCD calculations, allow a precise determination of $\alpha_{s}(Q)$ in three $Q~2$-intervals. The values are consistent with a running of $\alpha_{s}(Q)$, as expected from QCD. Extrapolating to $Q=M_{Z~0}$ yields $\alpha_{s}(M_{Z~0}) = 0.117\pm0.005(stat)~{+0.004}_{-0.005}(syst_{exp}) {\pm0.007}(syst_{theory})$.
2+1 jet rate as a function of ycut the jet algorithm cut-off value. Statistical errors only.
Measured values of Lambda-QCD in the MS Bar scheme and alpha_s as a function of Q**2. The second systematic uncertainty is related to the theoretical uncertainties .
Strong coupling constant alpha_s extrapolated to the Z0 mass.
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