New Angles on Energy Correlators

Abstract: Energy correlators have recently come to the forefront of jet substructure studies at colliders due to their remarkable properties: they naturally separate physics at different scales, are robust to contamination from soft radiation, and offer a direct connection with quantum field theory. The current parametrization used for energy correlators, however, is based on redundant pairwise angles with complex phase space restrictions. In this Letter, we introduce a new parametrization of energy correlators that features a simpler phase space structure and preserves information about the orientation of jet constituents. Further, our parametrization drastically reduces the computational cost to compute energy correlators on experimental data; whereas the time to compute a traditional projected $N$-point energy correlator scales as $M^N/N!$ on a jet with $M$ particles, our new parametrization achieves a scaling of $M^2 \log M$, remarkably independently of N. Even for N=3, this improved scaling is particularly important for studies of heavy ion collisions, and higher values of $N$ will enable new qualitative understanding of gauge theories. Theoretical calculations for our new energy correlators differ from those of traditional parametrizations only at next-to-next-to-leading logarithmic accuracy and beyond, and we expect that our simpler phase space structure will simplify those calculations. We also discuss how to extend our parametrization to resolved $N$-point energy correlators that encode angular distances between greater numbers of particles, yielding intuitive visualizations of jet substructure that are qualitatively different for different jet samples. We propose two possible generalizations for probing multi-prong jets and testing jet scaling behavior.