Generalized Detectors at Colliders

Abstract

Recent progress in collider physics has reformulated phenomenological questions in terms of detector correlation functions and advanced their theoretical understanding. These advances have primarily focused on correlators of the average null energy operator, $\mathcal{E}(\vec{n})$, known as energy correlators. However, colliders have access to a much broader class of detector operators, $\mathcal{E}^n_R(\vec{n})$, which measure powers of the energy on a subset of hadrons $R$, such as charged hadrons. These generalized detectors are generically not infrared and collinear safe, and their description requires nonperturbative matching between the hadronic detectors measured in the infrared and the partonic detectors used in ultraviolet calculations. We develop a framework for computing their multi-point correlation functions. We introduce universal nonperturbative matching coefficients, termed "detector functions", that implement this infrared-ultraviolet matching. For the $\mathcal{E}_R^n$ operators studied here, these coefficients are represented by energy-weighted moments of single- and multi-hadron fragmentation functions. We present their renormalization group structure, derive QCD factorization theorems for the projected correlators, and compute jet functions through next-to-leading order. In the fixed-coupling pure Yang-Mills limit, we derive the light-ray OPE of hadronic detectors and connect it to the QCD factorization framework. We also identify universal nonperturbative power corrections generated by soft radiation, which are enhanced in the collinear limit and can substantially modify the perturbative angular scaling. A parton shower study finds qualitative agreement with the predicted perturbative and nonperturbative scaling behaviors. Our work significantly broadens the space of detector operators under theoretical control, with potential phenomenological applications.