NEXT-TO-LEADING-ORDER QCD CORRECTIONS TO JET CROSS-SECTIONS AND JET RATES IN DEEPLY INELASTIC ELECTRON-PROTON SCATTERING

Jet cross sections in deeply inelastic scattering in the case of trans verse photon exchange for the production of (1+1) and (2+1) jets are c alculated in next-to-leading-order QCD (here the ''+1'' stands for the target remnant jet, which is included in the jet definition). The jet definition scheme is based on a modified JADE cluster algorithm. The calculation of the (2+1) jet cross section is described in detail. Res ults for the virtual corrections as well as for the real initial- and final-state corrections are given explicitly. Numerical results are st ated for jet cross sections as well as for the ratio sigma(2+1)jet/sig ma(tot) that can be expected at E665 and DESY HERA. Furthermore the sc ale ambiguity of the calculated jet cross sections is studied and diff erent parton density parametrizations are compared.