Factorization for Collider Dataspace Correlators

A metric on the space of collider physics data enables analysis of its geometrical properties, like dimensionality or curvature, as well as quantifying the density with which a finite, discrete ensemble of data samples the space. We provide the first systematically-improvable precision calculations on this dataspace, presenting predictions resummed to next-to-leading logarithmic accuracy, using the Spectral Energy Mover's Distance (SEMD) as its metric. This is accomplished by demonstration of factorization of soft and collinear contributions to the metric at leading power and renormalization group evolution of the single-scale functions that are present in the factorization theorem. As applications of this general framework, we calculate the two-point correlator between pairs of jets on the dataspace, and the measure of the non-Gaussian fluctuations in a finite dataset. For the non-Gaussianities, our calculations validate the existence of a universal structure that had been previously observed in simulated data. As byproducts of this analysis, we also calculate the two-loop anomalous dimension of the SEMD metric and show that the original Energy Mover's Distance metric is identical to the SEMD through next-to-next-to-leading logarithmic accuracy.