Theoretical and practical progresses in the HAL QCD method

S. Aoki
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引用次数: 2

Abstract

In this report, we discuss some theoretical and practical progresses in the HAL QCD potential method. We first clarify the issue of the derivative expansion for the non-local potential in the HAL QCD method. As the non-local potential in the original literature is not uniquely defined, we propose a procedure to define a non-local potential from NBS wave functions in terms of the derivative expansion. We then demonstrate how this definition works by using quantum mechanics with a separable potential. Secondly we discuss an issue of Hermiticity of the HAL QCD potential. Since the NBS wav functions are not orthogonal to each other in general, the HAL QCD potential is necessary to be non-Hermitian. We consider the next-to-leading order potential, which can be made Hermitian exactly by the change of variables. In general we can also make the higher order HAL QCD potential Hermitian order by order in the derivative expansion. An explicit example on how the procedure works is given for lattice QCD calculations. Finally we discuss how we can extract the HAL QCD potential from the NBS wave function in the boosted system. An explicit formula for this is derived.
HAL QCD方法的理论与实践进展
本文讨论了HAL QCD势方法的一些理论和实践进展。我们首先澄清了HAL QCD方法中非局部势的导数展开问题。由于原始文献中的非局部势不是唯一定义的,我们提出了一种根据导数展开从NBS波函数定义非局部势的方法。然后我们通过使用具有可分离势的量子力学来演示这个定义是如何工作的。其次,我们讨论了HAL QCD势的厄密性问题。由于NBS波函数通常不是相互正交的,HAL QCD势必须是非厄米势。我们考虑次阶势,它可以通过变量变换精确地变成厄米势。一般来说,我们也可以在导数展开式中使高阶的HAL QCD电位逐阶地厄米化。给出了晶格QCD计算的一个明确的例子。最后讨论了如何从升压系统的NBS波函数中提取HAL QCD势。为此导出了一个显式公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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