Observables for the Analysis of Event Shapes in e+ e- Annihilation and Other Processes

We present a set of rotationally invariant observables which characterizes the ''shapes'' of events, and is calculable in quantum-chromodynamics perturbation theory for final states consisting of quarks and gluons (G). We include the effects of fragmentation to hadrons in comparing the shapes of events from the processes e/sup +/e/sup -/ ..-->.. qq-bar, e/sup +/e/sup -/ ..-->.. qq-barG, and e/sup +/e/sup -/ ..-->.. heavy resonance ..-->.. GGG, and from heavy-quark and lepton production. We indicate how our analysis may be extended to deep-inelastic lepton-hadron interactions and hadron-hadron collisions involving large transverse momenta.