Wilson loops to 20th order numerical stochastic perturbation theory
Wilson loops to 20th order numerical stochastic perturbation theory
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Wilson 循环到 20 阶数值随机微扰理论
DOI：
10.1103/physrevd.86.054502
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发表时间：
2012
影响因子：
5
通讯作者：
A. Schiller
中科院分区：
文献类型：
--
作者：
R. Horsley;G. Hotzel;E. M. Ilgenfritz;R. Millo;Y. Nakamura;H. Perlt;P. E. L. Rakow;G. Schierholz;A. Schiller
我们使用数值随机微扰理论技术，计算不同尺寸的威尔逊环在纯晶格规范理论中对威尔逊规范作用的不同晶格尺寸的微扰贡献，最高可达 20 阶。这使我们能够研究微扰理论高阶下各种威尔逊环的微扰级数。我们观察到该系列的行为差异是循环顺序的函数。到目前为止，我们还没有找到通常被认为表征渐近级数的展开系数的阶乘增长的证据。根据实际观察到的行为，我们对由超几何函数参数化的模型中的序列进行求和。对于中等大小的威尔逊环，增强微扰理论中的总和系列已经达到中等微扰阶数的稳定平台。由于超几何模型对原始级数的系数进行平滑处理，增强级数中的系数变得更加稳定。我们引入不同大小的威尔逊环的广义比率。与标准蒙特卡罗测量中相应的威尔逊环一起，它们使我们能够评估其非扰动部分。
We calculate perturbative contributions of Wilson loops of various sizes up to order 20 inpure lattice gauge theory at different lattice sizes for the Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high orders of the perturbation theory. We observe differences in the behavior of the series as a function of the loop order. Up towe do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. For Wilson loops of moderate sizes the summed series in boosted perturbation theory reach stable plateaus for moderate perturbative order already. The coefficients in the boosted series become much more stable in the result of smoothing the coefficients of the original series effected by the hypergeometric model. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their nonperturbative parts.
DOI：
--
发表时间：
1973
期刊：
影响因子：
--
作者：
T. Banks
通讯作者：
T. Banks