arXiv 0812.22512008-12hep-lat

Wilson费米子在π区的观测

Observations on the Wilson fermions in the epsilon regime

Andrea Shindler

备注：: 17 pages, 1 figure. v2: few typos corrected. Published on PLB
发表信息：: Phys.Lett.B672:82-88,2009
DOI：: 10.1016/j.physletb.2008.12.061

摘要：

我们提出了几个意见，关于低夸克质量区与威尔逊费米子，这是如何与连续介质中的夸克制度。在有限格点间距下，如果我们降低夸克质量，一般情况下威尔逊费米子会发生从微小的截断效应到相当大的离散误差的转变。我们认为，这两个地区表现出相当不同的行为之间的耦合截止效应和零模式。我们在这两个制度之间插入添加到连续介质的制度公式，在Symanzik扩展的精神，相关运营商参数化的领先的截止效应。我们计算了配分函数、手征凝聚、标量和赝标量关联函数。最终公式可用于拟合点阵数据，以提取物理低能常数，并估计来自离散误差的系统不确定性。此外，他们提出了如何消除这些截止效应的方法，其核心是由连续零模捕获。

英文摘要：

We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the epsilon regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum epsilon regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.

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英文摘要：

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