Failure of naive parton models for inclusive electron-positron annihilation

The asymptotic scaling behavior of inclusive electron-positron annihilation, $e^{-}{e}^{+}\to \mathrm{nX}$, is discussed in the context of parton models. We show that, unlike processes governed by the short-distance structure of current products, the naive perturbation theory prediction for this reaction is not generally correct and, in particular, is not correct for a quark-gluon gauge theory. Drawing on the "solvable" model of quantum chromodynamics in two space-time dimensions, we construct a simple example which differs from expectations based on free quarks but which, paradoxically, not only scales but even satisfies Feynman's interpretation of the scaling emission of hadrons by quarks.