Energy correlations in electron-positron annihilation in quantum chromodynamics: Asymptotically free perturbation theory

In the absence of infrared mass singularities, the asymptotic behavior of cross sections for $e^{+}{e}^{-}$ annihilation in quantum chromodynamics can be expressed entirely in terms of the energy dependence of the renormalization-group running coupling constant. Since the theory is asymptotically free, the running coupling vanishes at high energy, and such infrared-finite cross sections can be calculated perturbatively. We extend previous work by calculating, through second order, the energy-weighted angular correlations of the hadrons produced in $e^{+}{e}^{-}$ annihilation. This involves the computation of quark-antiquark-gluon production and the correction to the lowest-order quark-antiquark production from virtual gluon exchange. A dimensional-continuation scheme is employed to establish that these correlations, taken in a distribution-theory sense, are indeed free of mass singularities. The correlations exhibit interesting features which vanish slowly ($\propto \frac{1}{\ln W}$) as the energy $W$ increases. We estimate that the nonperturbative, confinement contributions to these features vanish much more rapidly ($\propto \frac{1}{W^2}$). Thus, effects characteristic of quantum chromodynamics should be quite evident at high energies.