Electron-positron annihilation energy pattern in quantum chromodynamics: Asymptotically free perturbation theory

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Abstract
High-energy cross sections of quantum chromodynamics can be computed entirely in terms of the renormalization-group running coupling constant if these cross sections have no infrared mass singularities. Since the theory is asymptotically free, at high energies the running coupling constant vanishes and such cross sections can be computed perturbatively. Thus the theory of quantum chromodynamics may be rigorously tested. We compute the angular distribution of the hadronic energy produced in high-energy electron-positron annihilation to second order and find no mass singularities. Our result can be interpreted in terms of a jet opening angle which vanishes logarithmically as the energy increases. We compute phenomenologically the corrections to the energy pattern resulting from nonperturbative confinement effects. They become small at the energies of the colliding-beam machines now under construction.