Non-Gaussianities in Collider Metric Binning

Abstract

Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with probability 1, and so this suggests a method to search for and identify new physics by the deviation of measurement from a null hypothesis prediction. To quantify the deviation statistically, we directly calculate the probability distribution of the number of event pairs that land in the bin a fixed distance apart. This distribution is not generically Gaussian and the ratio of the standard deviation to the mean entries in a bin scales inversely with the square-root of the number of events in the data ensemble. If the dataspace manifold exhibits some enhanced symmetry, the number of entries is Gaussian, and further fluctuations about the mean scale away like the inverse of the number of events. We define a robust measure of the non-Gaussianity of the bin-by-bin statistics of the distance distribution, and demonstrate in simulated data of jets from quantum chromodynamics sensitivity to the parton-to-hadron transition and that the manifold of events enjoys enhanced symmetries as their energy increases.

Figures (3)

• Figure 1: Plots of the ratio of the standard deviation $\sigma_\epsilon$ of the number of pairs of events in the bin about distance $\epsilon$ to the mean number of pairs $\langle N_\epsilon\rangle$, as a function of the total number of points $n$ sampled on the unit line.
• Figure 2: Plot of the mean number of pairs of jets $\langle N_\epsilon\rangle$ as a function of their SEMD metric distance $\epsilon$ apart.
• Figure 3: Plot of the non-Gaussianity measure $\eta_\text{n-G}(\epsilon)$ on the simulated jet samples as a function of SEMD metric distance $\epsilon$. The approximate locations of the distances at and below which non-perturbative physics dominates $\epsilon_\text{np}$ is identified on each curve.