论文标题
HAL QCD方法中的理论和实际进步
Theoretical and practical progresses in the HAL QCD method
论文作者
论文摘要
在本报告中，我们讨论了HAL QCD潜在方法中的一些理论和实际进步。我们首先阐明了HAL QCD方法中非本地电位的导数扩展问题。由于原始文献中的非本地潜力不是唯一的定义，因此我们提出了一种程序，以根据衍生化扩展来定义NBS波函数的非本地潜能。然后，我们通过使用具有可分离势的量子力学来证明该定义如何工作。其次，我们讨论了HAL QCD潜力的墓穴性问题。由于NBS WAV函数一般不是彼此正交的，因此HAL QCD电势对于非热者是必不可少的。我们考虑了次要的订单潜力，这可以通过变量的变化来使其恰好使Hermitian造成。通常，我们还可以按衍生物扩展中的顺序使高阶HAL QCD潜在的Hermitian秩序。针对晶格QCD计算给出了有关该过程如何工作的明确示例。最后，我们讨论如何从增强系统中的NBS波函数中提取HAL QCD电位。得出了一个明确的公式。
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.
