Order alpha_s² QCD corrections to inclusive jet production in deep inelastic scattering

We analyze the order alpha_s^2 corrections to the single inclusive jet cross section in lepton-nucleon deep inelastic scattering. The full calculation is done analytically, in the small cone approximation, obtaining finite NLO partonic level cross sections for these processes. A detailed study of the different underlying partonic reactions is presented focusing in the size of the corrections they get at NLO accuracy, their relative weight, and the residual scale uncertainty they leave in the full cross section depending on the kinematical region explored. The dominant partonic process in very forward jet production is found to start at order alpha_s^2, being effectively a lowest order estimate, with the consequent large factorization scale uncertainty, and the likelihood of non-negligible corrections at the subsequent order in perturbation theory.