Observables for the Analysis of Event Shapes ine+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 $e^{+}{e}^{-}\to q\overline{q}$, $e^{+}{e}^{-}\to q\overline{q}G$, and $e^{+}{e}^{-}\to \mathrm{heavy}\mathrm{resonance}\to \mathrm{GGG}$, and from heavy-quark and lepton production. We indicate how our analysis may be extended to deep-elastic lepton-hadron interactions and hadron-hadron collisions involving large transverse momenta.