Next-to-leading-logarithmic parton shower in deep-inelastic scattering

We develop a next-to-leading-logarithmic parton shower in deep-inelastic scattering. The new model includes all kinds of next-to-leading-logarithmic corrections in the nonsinglet sector. It gives a definite scheme for QCD scale parameter Λ. Also it is possible to analyze final distributions of hadrons for obtaining Λsub(anti M anti S). In order to include the corrections, we extend the jet calculus to the space-like case. Then we calculate three-body functions for the spacelike decay. In addition to extensive analyses of the scale breaking of the structure function, we study the three-jet fractions using the cluster algorithm and the energy flow distributions. (orig.)