Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method
Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method
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晶格 QCD 中的重子相互作用：直接法与 HAL QCD 势法
DOI：
10.22323/1.256.0107
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
for Hal Qcd Collaboration
中科院分区：
文献类型：
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作者：
T. Iritani;for Hal Qcd Collaboration
我们以2+1味QCD中$m_\pi= 0.51$ GeV处的$\Xi\Xi$系统为例，分别使用涂抹夸克源和壁夸克源，对重子-重子相互作用的直接方法和HAL QCD势法进行了详细的比较。直接方法中的能量位移$\Delta E_\mathrm{eff}(t)$显示了对夸克源算子选择的强烈依赖，这意味着使用任何一个（或两个）源的结果都是错误的。另一方面，时间相关的HAL QCD方法给出了与夸克源无关的$\Xi\Xi$势，这要归功于势的导数展开，它将源依赖性吸收到下一个阶改正。HAL QCD势预测了$m_\pi= 0.51$ GeV处$\Xi\Xi$ （$^1$ S $_0$）通道中不存在束缚态，这也被有限体积能量的体积依赖性所证实。我们还证明了假平台在$t \sim 1$ fm处的有效能量位移$\Delta E_\mathrm{eff}(t)$的起源可以通过由HAL QCD势导出的有限体积上的几个低洼特征函数和特征值来澄清，这意味着$\Xi\Xi$ （$^1$ S $_0$）的基态饱和需要$t \sim 10$ fm在$(4.3 \ \mathrm{fm})^3$晶格上的散射源的直接方法。而HAL QCD方法则不存在这样的问题。
We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\Xi\Xi$ system at $m_\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources. The energy shift $\Delta E_\mathrm{eff}(t)$ in the direct method shows the strong dependence on the choice of quark source operators, which means that the results with either (or both) source are false. The time-dependent HAL QCD method, on the other hand, gives the quark source independent $\Xi\Xi$ potential, thanks to the derivative expansion of the potential, which absorbs the source dependence to the next leading order correction. The HAL QCD potential predicts the absence of the bound state in the $\Xi\Xi$($^1$S$_0$) channel at $m_\pi= 0.51$ GeV, which is also confirmed by the volume dependence of finite volume energy from the potential. We also demonstrate that the origin of the fake plateau in the effective energy shift $\Delta E_\mathrm{eff}(t)$ at $t \sim 1$ fm can be clarified by a few low-lying eigenfunctions and eigenvalues on the finite volume derived from the HAL QCD potential, which implies that the ground state saturation of $\Xi\Xi$($^1$S$_0$) requires $t \sim 10$ fm in the direct method for the smeared source on $(4.3 \ \mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such a problem.