Monte Carlo approach to QCD jets in the next-to-leading-logarithmic approximation

We present a Monte Carlo model for the parton generation in the next-to-leading-logarithmic (NLL) approximation. This model provides us with the natural introduction of cross sections for nontrivial hard scatterings and it enables us to determine the scheme for the fundamental parameter Λ in QCD. The implementation of the NLL effects into the Monte Carlo approach is studied extensively. The stochastic treatment requires the positivity of functions for hard scatterings, two-body decays, and three-body decays. This leads to the condition of angular ordering which restricts the phase space. We apply this model to $e^{+}$ $e^{\mathrm{-}}$ annihilation and incorporate clean three-jet events into the QCD cascade.