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arXiv 0705.3322hep-lat
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ε区双味格点量子色动力学与手征随机矩阵理论

Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory

JLQCD, TWQCD collaboration, :, H. Fukaya, S. Aoki, T. W. Chiu, S. Hashimoto, T. Kaneko, H. Matsufuru, J. Noaki, K. Ogawa, T. Onogi, N. Yamada

摘要:

QCD Dirac算符在ε区域的低本征值谱与手征随机矩阵理论(ChRMT)的谱相匹配。我们研究这种对应的情况下,包括海夸克进行双味QCD模拟的晶格。使用重叠费米子公式,它在有限的晶格间距下保持精确的手征对称性,我们在16 ^3 \times 32晶格上将海夸克质量推低到\sim 3 MeV,晶格间距为\simeq 0.11 fm。我们比较低的本征值分布,并找到一个很好的协议与分析预测的ChRMT。通过匹配最低的本征值,我们得到了手征凝聚体,π(2 GeV)[MSbar] = [251(7)(11)MeV]^3,其中的误差表示π展开中的统计效应和高阶效应。我们还计算了两种格点间距下重海夸克的本征值分布。虽然这些海夸克没有采用狄拉克展开式,但我们发现狄拉克算符谱与ChRMT有着合理的一致性。外推到手性极限后,Sigma的值与ε-区的估计值一致。

英文摘要:

The low-lying eigenvalue spectrum of the QCD Dirac operator in the epsilon-regime is expected to match with that of chiral Random Matrix Theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor QCD simulations on the lattice. Using the overlap fermion formulation, which preserves exact chiral symmetry at finite lattice spacings, we push the sea quark mass down to \sim 3 MeV on a 16^3\times 32 lattice at a lattice spacing a \simeq 0.11 fm. We compare the low-lying eigenvalue distributions and find a good agreement with the analytical predictions of ChRMT. By matching the lowest-lying eigenvalue we extract the chiral condensate, Σ(2 GeV)[MSbar] = [251(7)(11) MeV]^3, where errors represent statistical and higher order effects in the epsilon expansion. We also calculate the eigenvalue distributions on the lattices with heavier sea quarks at two lattice spacings. Although the epsilon expansion is not applied for those sea quarks, we find a reasonable agreement of the Dirac operator spectrum with ChRMT. The value of Sigma, after extrapolating to the chiral limit, is consistent with the estimate in the epsilon-regime.

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