Non-Gaussianities in Collider Metric Binning
This work addresses the challenge of identifying new physics in particle collider experiments for physicists, but it appears incremental as it builds on existing metric-based methods by focusing on non-Gaussian statistical properties.
The paper tackled the problem of detecting new physics in particle collider data by analyzing the distribution of pairwise distances between events, finding that deviations from expected distributions can indicate novel phenomena, with sensitivity demonstrated in simulated jet data to the parton-to-hadron transition and enhanced symmetries at higher energies.
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.