The Efficacy of Event Isotropy as an Event Shape Observable

Abstract

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.

Comments: 31 pages, 19 figures