Energy Correlators in $V + X$ as a Benchmark Observable for Precision QCD

Abstract

We propose projected energy correlators measured on the recoiling QCD radiation of a $Z/\gamma$ as a benchmark observable for precision QCD at the LHC. Using the $Z/\gamma$ as a hard scale prevents the need for a jet algorithm, simplifying both the perturbative and non-perturbative corrections. We develop a framework to combine state-of-the-art fixed-order amplitudes, high order resummation, and universal non-perturbative matrix elements. Our approach is based on numerically computed inclusive hard functions, allowing flexibility in the process and the inclusion of realistic experimental cuts. We perform detailed numerical studies of the projected energy correlators at next-to-leading order + next-to-next-to-leading logarithm (NLO+NNLL) to verify the stability of our setup. We present numerical results at NLO+NNLL, which are the first complete matched predictions for energy correlators at the LHC at this order. We discuss the prospects for extensions to higher orders, outlining a path to NNLO calculations of energy correlators at the LHC.