标题： 能量-能量关联函数在强子对撞机上的研究：全息块和奇点 显示英文标题

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

摘要： 能量-能量关联函数（EEC）是一种事件形状可观测量，用于表征碰撞事件中能量流的分布。 我们开始研究强子对撞机上的全范围EEC，推广了在$e^+e^-$碰撞中广泛研究的EEC以及强子碰撞中的横向EEC。 我们从洛伦兹对称性推导出天体块，以对强子对撞机上的EEC进行部分波分解。 这些天体块本质上是二维天体球面上的共形块，它们还额外依赖于沿碰撞轴的“光束跃迁矩阵”共线自旋。 在本工作中，我们在纯杨-米尔斯理论中进行了该可观测量的一阶（LO）解析计算，并以此为例说明块分解。 数值上，块展开在共线极限下相比传统的幂级数展开表现出更高的准确性。 解析上，我们在这个例子中观察到，块系数在共线和横向自旋中都表现出解析性。 此外，我们分析了几个LO下的运动学极限——共线、背对背、相反共面和Regge极限。 虽然前三个极限自然地推广了其$e^+e^-$碰撞对应物或横向EEC，并由软-共线动力学支配，但Regge极限需要完整的角度依赖性并揭示了BFKL物理。 从现象学角度来看，我们提出了一种现实的实验设置，并简要讨论了部分子分布函数的卷积如何修改微扰EEC结果。 我们的工作表明，强子对撞机上的全范围EEC是一个优雅的可观测量，它探测更广泛的运动学空间，并通过单一测量连接不同QCD动力学的各种区域。 显示英文摘要

摘要： 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.