arXiv 2104.005882021-04nucl-th

Q累积量的$v_{n}\{2k\}$谐波的统计不确定性

Statistical uncertainties of the $v_{n}\{2k\}$ harmonics from Q-cumulants

L. Nadderd, J. Milosevic, F. Wang

备注：: 8 pages, 9 figures
发表信息：: Phys. Rev. C 104, 034906 (2021)
DOI：: 10.1103/PhysRevC.104.034906

摘要：

给出了计算从Q累积量中提取的$v_{n}\{2k\}$谐波的统计不确定度的解析公式。Q累积量是$2m$ -粒子方位角相关性的加权平均值$\llangle 2m \rrangle$的多元多项式函数。$\llangle 2m \rrangle$的方差和协方差包含在不确定度的解析公式中，可以与$v_{n}\{2k\}$谐波的计算同时计算。计算使用一个简单的玩具模型，大致模拟椭圆流方位各向异性的幅度约为0.05。结果进行了比较，得到的结果由许多数据子集，并通过自举方法。第一种是在实际实验中估计$v_{n}\{2k\}$谐波的统计不确定度的常用方法。为了提高$v_{n}\{2k\}$谐波测量的精度，在自举方法中使用了大量的15000个子集和相同数量的重采样。与所提出的$v_{n}\{2k\}$统计不确定度的解析计算方法进行了比较，两者吻合很好，并给出了Q累积量计算的递推公式。

英文摘要：

Analytic formulas to calculate statistical uncertainties of $v_{n}\{2k\}$ harmonics extracted from the Q-cumulants are presented. The Q-cumulants are multivariate polynomial functions of the weighted means of $2m$-particle azimuthal correlations, $\llangle 2m \rrangle$. Variances and covariances of the $\llangle 2m \rrangle$ are included in the analytic formulas of the uncertainties that can be calculated simultaneously with the calculations of the $v_{n}\{2k\}$ harmonics. The calculations are performed using a simple toy model which roughly simulates elliptic flow azimuthal anisotropy with magnitudes around 0.05. The results are compared with the results obtained by the many data sub-sets, and by the bootstrapping method. The first one is a common way of estimation of the statistical uncertainties of the $v_{n}\{2k\}$ harmonics in a real experiment. In order to increase precision in the measurement of the $v_{n}\{2k\}$ harmonics, a large number of 15000 sub-sets and the same number of the re-sampling in the bootstrap method is used. A very good agreement in the comparison with the proposed way of the analytic calculation of the $v_{n}\{2k\}$ statistical uncertainties is found. Additionally, a recurrence equation for Q-cumulants calculation is also presented.

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。

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英文摘要：

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