Inclusive jet cross sections in the Breit frame in neutral current deep inelastic scattering at HERA and determination of alpha_s

Inclusive jet differential cross sections have been measured in neutral current deep inelastic e+p scattering for boson virtualities Q**2>125 GeV**2. The data were taken using the ZEUS detector at HERA and correspond to an integrated luminosity of 38.6 pb-1. Jets were identified in the Breit frame using the longitudinally invariant K_T cluster algorithm. Measurements of differential inclusive jet cross sections are presented as functions of jet transverse energy (E_T,jet), jet pseudorapidity and Q**2, for jets with E_T,jet>8 GeV. Next-to-leading-order QCD calculations agree well with the measurements both at high Q**2 and high E_T,jet. The value of alpha_s(M_Z), determined from an analysis of dsigma/dQ**2 for Q**2>500 GeV**2, is alpha_s(M_Z) = 0.1212 +/- 0.0017 (stat.) +0.0023 / -0.0031 (syst.) +0.0028 / -0.0027 (th.).