The efficacy of event isotropy as an event shape observable

Event isotropy $\mathcal{I}^\text{sph}$, an event shape observable that measures the distance of a final state from spherically symmetric state, is designed for new physics signals are far QCD-like. Using technique producing wide variety can range near-spherical to jetty, we compare other observables. We show thrust $T$ and $C$ parameter (and $\lambda_\text{max}$, largest eigenvalue sphericity matrix) strongly correlated thus redundant, good approximation. By contrast, adds considerable information, often serving break degeneracies between would have almost identical distributions. Signals with broad distributions in (or $\lambda_\text{max}$) $\mathcal{I}^\text{sph}$ separately much narrower distributions, more easily distinguished, $({\mathcal{I}^\text{sph}},\lambda_\text{max})$ plane. An intuitive, semi-analytic estimation clarifies why this case assists interpretation