We propose a new scheme for a QCD cascade model in the lightlike axial gauge. In this new scheme the valence antiquark can evolve as well as the valence quark, while in the conventional scheme with the lightlike axial gauge only the valence quark evolves. Since the proposed scheme is formulated in terms of well-defined variables, we can apply this scheme to the next-to-leading-logarithmic model in $e^{+}$$e^{\mathrm{-}}$ annihilation. We show that new and conventional schemes give us the same results for energy distributions of the quark and for emission probabilities for gluons.

• Received 8 August 1988

DOI:https://doi.org/10.1103/PhysRevD.39.156