FastEEC：N点能量关联器的快速评估
FastEEC: Fast Evaluation of N-point Energy Correlators
AI总结：
针对N点能量关联器计算量大的问题，提出基于尺度分离和动态子喷注重构半径的快速近似方法，大幅加速计算，并支持高次幂正则化，附有公开代码。
摘要：
能量关联器刻画了对撞机产生的散射事件中的渐近能量流，从中可以推断出散射的微观物理。这种对碰撞的视角类似于对宇宙微波背景的分析，并且已经确定了能量关联器的一系列有前景的唯象应用，包括对强子化、死锥效应、测量$\alpha_s$和顶夸克质量的研究。虽然对于较大的$N$值，$N$点能量关联器的研究很有趣，但它们的评估计算量很大，其规模为$M^N/N!$，其中$M$是粒子数。在这封信中，我们开发了一种快速、近似的方法来评估它们，利用在给定角尺度上的关联对其他（广泛分离的）尺度上的效应不敏感这一事实。这意味着能量关联器可以在（子）喷注上计算，从而有效减少$M$。此外，我们利用动态的（子）喷注重构半径，使我们能够在不限制所探测的角尺度的情况下获得可靠的结果。具体来说，我们关注投影能量关联器，它投影到$N$个方向之间的最大分离上。例如，对于$N=7$，我们发现根据所需精度，加速可达四个数量级。我们还考虑了在能量关联器中将能量提高到大于一的幂的可能性，这已被提出用于降低软灵敏度，并进一步缩短所需的计算时间。这些高次幂关联器不是共线安全的，但作为副产品，我们的方法提出了一种自然的正则化方法，使它们可以用微扰理论来描述。这封信附有一个实现我们方法的公共代码。
英文摘要：
Energy correlators characterize the asymptotic energy flow in scattering events produced at colliders, from which the microscopic physics of the scattering can be deduced. This view of collisions is akin to analyses of the Cosmic Microwave Background, and a range of promising phenomenological applications of energy correlators have been identified, including the study of hadronization, the deadcone effect, measuring $α_s$ and the top quark mass. While $N$-point energy correlators are interesting to study for larger values of $N$, their evaluation is computationally intensive, scaling like $M^N/N!$, where $M$ is the number of particles. In this Letter, we develop a fast, approximate method for their evaluation exploiting that correlations at a given angular scale are insensitive to effects at other (widely-separated) scales. This implies that the energy correlator can be computed on (sub)jets, effectively reducing M. Furthermore, we utilize a dynamical (sub)jet radius that allows us to obtain reliable results without restricting the angular scales being probed. For concreteness we focus on the projected energy correlator, which projects onto the largest separation between the $N$ directions. E.g.~for $N=7$ we find a speed up of up to four orders of magnitude, depending on the desired accuracy. We also consider the possibility of raising the energy to a power higher than one in the energy correlator, which has been proposed to reduce soft sensitivity, and further cuts back the required computation time. These higher-power correlators are not collinear safe, but as a byproduct our approach suggests a natural method to regularize them, such that they can be described using perturbation theory. This letter is accompanied by a public code that implements our method.
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