Energy-Energy Correlator at Hadron Colliders: Celestial Blocks and Singularities

Energy-energy correlator (EEC) is an event shape observable that characterizes the distribution of energy flux in collision events. We initiate the study of full-range EEC at hadron colliders, generalizing the extensively studied EEC in $e^+e^-$ collision as well as the transverse EEC in hadron collisions. We derive celestial blocks from Lorentz symmetry to perform partial wave decomposition of the EEC at hadron colliders. These celestial blocks are essentially conformal blocks on the 2d celestial sphere, which have additional dependence on the collinear spin of ``light-ray transition matrix'' along the collision axis. In this work, we perform the first leading-order (LO) analytic calculation of this observable in pure Yang-Mills theory and use it as an example to illustrate the block decomposition. Numerically, the block expansion demonstrates superior accuracy in the collinear limit compared to conventional power series expansion. Analytically, we observe in this example that the block coefficients exhibit analyticity in both collinear and transverse spin. In addition, we analyze several kinematic limits at LO -- collinear, back-to-back, opposite coplanar and Regge limit. While the first three limits naturally generalize their $e^+e^-$ collision counterparts or transverse EEC and are governed by soft-collinear dynamics, the Regge limit requires complete angular dependence and reveals BFKL physics. Phenomenologically, we propose a realistic experimental setup and briefly discuss how the convolution of parton distribution function modifies the perturbative EEC result. Our work suggests that the full-range EEC at hadron colliders is an elegant observable which probes a broader kinematic space and connects various regimes of different QCD dynamics through a single measurement.