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