arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2201.05166hep-phnucl-th
收藏

重整化群流与径迹函数矩

Renormalization Group Flows for Track Function Moments

Max Jaarsma, Yibei Li, Ian Moult, Wouter Waalewijn, Hua Xing Zhu

备注：
45 pages, 4 figures, 1 Mathematica Notebook, v2: journal version
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文推导了径迹函数矩的重整化群演化方程，利用能量守恒的平移对称性以累积量表述，并解析计算至第六矩的$\mathcal{O}(α_s^2)$阶，为LHC上基于径迹的高阶能量流关联研究奠定基础。

摘要：

径迹函数描述了夸克和胶子碎裂为带电强子的集体效应，使其成为强子对撞机上喷注子结构测量的关键要素，其中基于径迹的测量提供了优越的角分辨率。径迹函数的第一矩描述了带电粒子中沉积的平均能量，是一个简单且已被充分研究的对象。然而，对能量流的高阶关联的测量需要对强子化过程中的涨落进行表征，这在理论上由径迹函数的高阶矩描述。在本文中，我们推导了径迹函数矩的重整化群（RG）演化方程的结构。我们表明，能量守恒产生了一个平移对称性，使得演化方程可以用累积量$κ(N)$以及夸克和胶子径迹函数第一矩之差$Δ$来书写。前三个累积量的唯一性将其全阶演化固定为DGLAP形式，直至涉及$Δ$幂次的修正，这些修正对于唯象径迹函数在微扰展开中被数值抑制为有效阶。然而，在第四累积量及以上，存在非平凡的RG混合，例如$κ(4)$混合到$κ(2)^2$等累积量乘积中。我们解析计算了在$\mathcal{O}(α_s^2)$阶下直到第六矩的演化方程，并研究了相关的RG流。这些结果允许利用径迹研究能量流中高达六点关联，为LHC上的精密喷注子结构铺平了道路。

英文摘要：

Track functions describe the collective effect of the fragmentation of quarks and gluons into charged hadrons, making them a key ingredient for jet substructure measurements at hadron colliders, where track-based measurements offer superior angular resolution. The first moment of the track function, describing the average energy deposited in charged particles, is a simple and well-studied object. However, measurements of higher-point correlations of energy flow necessitate a characterization of fluctuations in the hadronization process, described theoretically by higher moments of the track function. In this paper we derive the structure of the renormalization group (RG) evolution equations for track function moments. We show that energy conservation gives rise to a shift symmetry that allows the evolution equations to be written in terms of cumulants, $κ(N)$, and the difference between the first moment of quark and gluon track functions, $Δ$. The uniqueness of the first three cumulants then fixes their all-order evolution to be DGLAP, up to corrections involving powers of $Δ$, that are numerically suppressed by an effective order in the perturbative expansion for phenomenological track functions. However, at the fourth cumulant and beyond there is non-trivial RG mixing into products of cumulants such as $κ(4)$ into $κ(2)^2$. We analytically compute the evolution equations up to the sixth moment at $\mathcal{O}(α_s^2)$, and study the associated RG flows. These results allow for the study of up to six-point correlations in energy flow using tracks, paving the way for precision jet substructure at the LHC.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑