FASTEEC Fast evaluation of N-point energy correlators

Energy correlators characterize the asymptotic energy flow in scattering events produced at colliders, from which the microscopic physics of the scattering can be deduced. This view of collisions is akin to analyzes of the Cosmic Microwave Background, and a range of promising phenomenological applications of energy correlators have been identified, including the study of hadronization, the deadcone effect, measuring α₈ and the top quark mass. While N-point energy correlators are interesting to study for larger values of N, their evaluation is computationally intensive, scaling like M^N/N!, where M is the number of particles. In this Letter, we develop a fast, approximate method for their evaluation exploiting that correlations at a given angular scale are insensitive to effects at other (widely-separated) scales. This implies that the energy correlator can be computed on (sub)jets, effectively reducing M. Furthermore, we utilize a dynamical (sub)jet radius that allows us to obtain reliable results without restricting the angular scales being probed. For concreteness, we focus on the projected energy correlator which projects onto the largest separation between the N directions. E.g. for N=7 we find a speed up of up to four orders of magnitude, depending on the desired accuracy. We also consider the possibility of raising the energy to a power higher than one in the energy correlator, which has been proposed to reduce soft sensitivity. These higher-power correlators are not collinear safe, but as a byproduct our approach suggests a natural method to regularize them, such that they can be described using perturbation theory. This Letter is accompanied by a public code that implements our method.