论文标题

晶格QCD和Baryon-Baryon互动:HAL QCD方法

Lattice QCD and baryon-baryon interactions: HAL QCD method

论文作者

Aoki, Sinya, Doi, Takumi

论文摘要

在本文中,我们回顾了HAL QCD方法,以研究晶格QCD中的核力量等重子 - 巴里昂相互作用。我们首先详细解释了我们的策略,以通过定义诸如QCD之类的现场理论中的潜力来研究巴里昂 - 巴里昂的相互作用。我们在QCD中引入了Nambu-bethe-salpeter(NBS)波函数,以低于非弹性阈值的两个重子。然后,我们根据衍生物膨胀来定义NBS波函数的电势,该衍生物的扩展可在非弹性阈值以下正确重现散射相移。使用此定义,我们制定了一种在晶格QCD中提取电势的方法。其次,我们通过将其与常规方法进行比较,讨论了HAL QCD方法的利弊,在该方法中,人们直接通过Lüscher的公式将散射相移来提取散射相移。我们给出了几种理论和数值证据,即传统方法与迄今为止文献中有限体积能量的天真高原拟合结合在一起,由于弹性激发态的污染物而无法处理重击 - 巴里昂的相互作用。另一方面,我们表明可以通过以能量无关的方式定义潜力来避免使用这种严重的问题。我们还讨论了HAL QCD方法的系统学,特别是与导数扩展的截断相关的误差。第三,我们提供了从HAL QCD方法获得的几个结果,其中包括(中央)核力量,张量,自旋轨道力和三个核素力。我们最终显示了在几乎物理派质量,$m_π\ simeq 146 $ meV上计算出的最新结果,其中包括导致$ω$和$nΩ$ dibaryons的超子力量。

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.

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