Energy Correlators of Spinning Sources

The $N$-point energy correlator measures the energy flux through $N$ detectors. We present a general framework that characterizes its full angular dependence in a series of \textit{spinning energy correlators}. These spinning correlators resurrect the angular momentum structure of both the source and the detector configuration, lost otherwise in inclusive measurements. We demonstrate that unitarity and energy positivity confine these correlators to a sharply bounded region, with the boundary realized by extremal correlators generated by pure spin states. We present a first calculation of spinning energy correlators in QCD as well as spinning energy-charge correlators. Their enhanced insensitivity to infrared dynamics opens up a new set of observables that directly probe the hard part of the scattering. Finally, we provide generalized sum rules, extended to spinning correlators and to conserved charges beyond energy.

💡 Research Summary

The paper introduces a comprehensive framework for restoring and classifying the full angular dependence of N‑point energy correlators when the source carries spin. Traditional energy‑energy correlators (EECs) average over detector orientations and thus erase information about the source’s polarization and the detector geometry. The authors resolve this loss by decomposing the 2 N detector directions into 2 N − 3 internal angles (z_{ij}= \frac{1}{2}(1-\cos\theta_{ij})) that encode the relative configuration of the detectors, and three Euler angles ((\Phi,\Theta,\varphi)) that describe the overall rigid‑body orientation of the detector set in space.

The central object is the density matrix of the N‑point correlator in a spin basis, \