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arXiv 1702.08174hep-lathep-ph
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$N_f=2$格点量子色动力学的球谱各向异性格点研究

Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices

Wei Sun, Long-Cheng Gui, Ying Chen, Ming Gong, Chuan Liu, Yu-Bin Liu, Zhaofeng Liu, Jian-Ping Ma, Jian-Bo Zhang

备注：
14 pages, 8 figures, 9 tables; typos fixed, minor modifications, match the published version
发表信息：
Chin.Phys. C42 (2018) no.9, 093103
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摘要：

利用$N_f=2$方法研究了各向异性格点上格点量子色动力学中的最低位胶球.我们在两个不同的和相对较重的夸克质量，相应的物理π介子质量为$m_π\sim 938$ MeV和$650$ MeV的模拟。夸克质量依赖的胶球质量还没有在本研究中进行了调查。在计算相应的关联函数时，只利用了由威尔逊圈构造的胶子算符。在张量通道中，我们得到在$m_π\sim 938$ MeV和$650$ MeV下基态质量分别为2.363（39）GeV和2.384（67）GeV.在赝标通道中，当使用连续极限为$ε_{ijk}TrB_iD_jB_k$的胶子算符时，我们得到了两个π质量下的基态质量分别为2.573（55）GeV和2.585（65）GeV.这些结果与淬火近似下的相应结果是一致的。相比之下，如果我们使用拓扑电荷密度作为赝标的场算符，最低态的质量要轻得多（约1 GeV），并且与味单重态$q\bar{q}$介子的预期质量相容。这表明算符$ε_{ijk}TrB_iD_jB_k$和拓扑电荷密度与胶球态和$q\bar{q}$介子的耦合是不同的。对轻味单重态赝标介子的观测可以看作是动力学夸克效应的表现。在标量通道中，由胶子算符的关联函数得到的基态质量约为1.4-1.5 GeV，与由夸克双线性算符的关联函数得到的基态质量接近.在所有情况下，胶球和常规介子之间的混合仍有待于未来进一步澄清。

英文摘要：

The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_π\sim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_π\sim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $ε_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $q\bar{q}$ meson. This indicates that the operator $ε_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $q\bar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.

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