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arXiv 2003.10730hep-lathep-phnucl-th
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格点量子色动力学和重子-重子相互作用：HAL QCD方法

Lattice QCD and baryon-baryon interactions: HAL QCD method

Sinya Aoki, Takumi Doi

备注：
39 pages, 20 figures, Contribution to Frontiers in Physics (Research topic) "The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future", Published version
发表信息：
Front. Phys. 8 (2020) 307
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摘要：

本文综述了用HAL QCD方法研究格点量子色动力学中的重子-重子相互作用，如核力。我们首先详细解释我们的策略，通过定义在场论，如QCD的潜力，调查重子重子相互作用。本文在非弹性阈值以下的重子量子色动力学中引入Nambu-Bethe-Salpeter（NBS）波函数。然后，我们定义的潜在的NBS波函数的衍生物的扩展，这是正确地再现低于非弹性阈值的散射相移。利用这个定义，我们给出了一种在格点量子色动力学中提取势的方法。其次，我们讨论了HAL QCD方法的优点和缺点，通过比较它与传统的方法，其中一个直接提取的散射相移的有限体积能量通过Lüscher的公式。我们给出了几个理论和数值证据，说明由于弹性激发态的污染，目前文献中结合有限体积能量的朴素平台拟合的传统方法不能用于重子-重子相互作用.另一方面，我们表明，这样一个严重的问题，可以避免在HAL QCD方法通过定义在一个能量无关的方式的潜力。我们还讨论了系统的HAL QCD方法，特别是与截断的衍生物展开的错误。第三，我们给出了用HAL QCD方法得到的几个结果，包括（中心）核力、张量力、自旋轨道力和三核子力。最后给出了在近物理π介子质量$m_π\simeq 146$ MeV下的最新计算结果，包括导致形成$ΩΩ$和$NΩ$重子的超子力.

英文摘要：

In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories such as QCD. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we formulate a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the Lüscher's formula. We give several theoretical and numerical evidences that the conventional method combined with the naive plateau fitting for the finite volume energies in the literature so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious problem can be avoided in the HAL QCD method by defining the potential in an energy-independent way. We also discuss systematics of the HAL QCD method, in particular errors associated with a truncation of the derivative expansion. Thirdly, we present several results obtained from the HAL QCD method, which include (central) nuclear force, tensor force, spin-orbital force, and three nucleon force. We finally show the latest results calculated at the nearly physical pion mass, $m_π\simeq 146$ MeV, including hyperon forces which lead to form $ΩΩ$ and $NΩ$ dibaryons.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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