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Jet production and measurements of $α\_S$ at HERA

The inclusive jet, dijet and trijet production cross-sections in deep-inelastic scattering (DIS) at $\sqrt{s}$=320GeV have been measured at the electron-proton collider HERA by the H1 and ZEUS collaborations using data taken in 1998-2000. The jet cross-sections have been measured differentially in four-momentum transfer squared $Q^2$ and jet transverse energy in the Breit-frame $E\_{T,B}$ with a typical precision of 5-10% limited by systematic uncertainties such as hadronization corrections and hadronic energy scale. All jet observables are well described by perturbative QCD ($\_pQCD$) predictions at next-to-leading order (NLO) within the estimated accuracy of these calculations which is limited by the absence higher orders, and which is in general inferior to the experimental precision. The values for the coupling constant $α\_S$ of the strong interaction as determined by fits of $\_pQCD$ predictions to the inclusive jet cross-section and the trijet-to-dijet production ratio $R\_{3/2}$ are consistent for both experiments and both observables, and also are in excellent agreement with the world average. Combining the individual measurements, a common value of $α\_S=0.1186\pm0.0011(exp.)\pm$0.0050(theory) is obtained.