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arXiv 1611.07643hep-latcond-mat.stat-mechcond-mat.str-elhep-phnucl-th
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关于格点量子色动力学中重子关联函数的统计

On the Statistics of Baryon Correlation Functions in Lattice QCD

Michael L. Wagman, Martin J. Savage

备注：
34 pages, 35 figures. Discussion of systematic uncertainties and extrapolation in Sec. IV and elsewhere expanded and clarified. Notation adjusted for clarity
发表信息：
Phys. Rev. D 96, 114508 (2017)
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摘要：

本文对用格点量子色动力学计算的单重子关联函数的结构进行了系统的分析，特别着重于表征量子涨落噪声的结构。在这些关联函数的信号噪声问题示出，作为长期怀疑，导致从一个符号的问题。对数振幅和复相位分别近似地服从正态分布和包裹正态分布。循环统计的属性被用来理解一个大的时间噪声区域的出现，标准的能量测量是不可靠的。重子关联函数分布中的幂律尾，与稳定分布和“Levy飞行”有关，被发现在它们的时间演化中起着核心作用。一种新的方法来分析关联函数被认为是信噪比的能量测量是恒定的，而不是指数下降，增加源-汇分离时间。这种新的方法包括一个额外的系统的不确定性，可以通过执行外推，和信号噪声问题重新出现在这个外推的统计。它表明，这种新的方法允许准确的结果，核子质量被提取的大时间噪声区域无法达到标准方法。这里提出的观测结果预计将适用于更普遍的量子蒙特卡罗计算。与这里介绍的方法类似的方法可能会导致对噪声较大系统的分析的实际改进。

英文摘要：

A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and "Levy flights", are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem re-emerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

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