将多粒子关联函数缩减到一定大小
Cutting Multiparticle Correlators Down to Size
摘要：
多粒子关联函数是量子场论和对撞机物理学中经常遇到的数学对象。通过将多粒子关联函数转换成图论的语言，我们可以获得对它们结构的新见解，并确定操纵它们的有效方法。在本文中，我们强调了这种图论方法的力量，通过“切开”图的顶点和边，使我们能够系统地分类多粒子关联函数间的线性关系，并开发更快的方法来计算它们。朴素的计算复杂性的$N$点相关器之间的$M$粒子是$\mathcal O(M^N)$，但当粒子之间的成对距离可以被铸造为一个内积，我们表明，所有这样的关联函数可以在线性$\mathcal O(M)$运行时计算。借助新的张量对象，称为能量流矩，我们实现了快速实施的射流子结构观测，如$C_2$和$D_2$，这是广泛使用的大型强子对撞机，以确定增强强子共振。作为另一个应用，我们计算了$d$边数最多为$d = 16$（15，641，159）的无叶多重图的个数，证明了这与次数为$d$的独立运动多项式的个数相同，以前只有$d=8$（279）知道。
英文摘要：
Multiparticle correlators are mathematical objects frequently encountered in quantum field theory and collider physics. By translating multiparticle correlators into the language of graph theory, we can gain new insights into their structure as well as identify efficient ways to manipulate them. In this paper, we highlight the power of this graph-theoretic approach by "cutting open" the vertices and edges of the graphs, allowing us to systematically classify linear relations among multiparticle correlators and develop faster methods for their computation. The naive computational complexity of an $N$-point correlator among $M$ particles is $\mathcal O(M^N)$, but when the pairwise distances between particles can be cast as an inner product, we show that all such correlators can be computed in linear $\mathcal O(M)$ runtime. With the help of new tensorial objects called Energy Flow Moments, we achieve a fast implementation of jet substructure observables like $C_2$ and $D_2$, which are widely used at the Large Hadron Collider to identify boosted hadronic resonances. As another application, we compute the number of leafless multigraphs with $d$ edges up to $d = 16$ (15,641,159), conjecturing that this is the same as the number of independent kinematic polynomials of degree $d$, previously known only to $d=8$ (279).
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