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arXiv 1406.4987hep-phhep-latnucl-th
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QCD Lite的手征对称性破缺

Chiral symmetry breaking in QCD Lite

Georg P. Engel, Leonardo Giusti, Stefano Lottini, Rainer Sommer

摘要:

QCD中存在自发手征对称性破缺的一个显著特征是Dirac算符的低模在原点附近的凝聚。在手征极限下,凝聚速率必须等于(Mpi ^2 Fpi ^2)/2相对于夸克质量m的斜率,其中Mpi和Fpi是南武-戈德斯通玻色子的质量和衰变常数。通过对含两个轻简并Wilson夸克的格点量子色动力学的数值模拟,计算了(厄米)Dirac算符的谱密度、夸克质量、赝标介子质量和衰变常数.我们使用CLS晶格在三个值的晶格间距在0.05-0.08微米的范围内,并为几个夸克质量对应的赝标介子质量下降到190兆电子伏。由于参数空间的覆盖,我们可以有信心地将所有量外推到手征极限和连续极限。结果表明,低夸克模在连续介质中确实发生了Banks-Casher机制所期望的凝聚,凝聚速率符合Gell-Mann-Oakes-Renner(GMOR)关系.对于重整化群不变量比,我们得到[^RGI]^(1/3)/F =2.77(2)(4)和λ ^MSbar/F = 3.6(2),如果用一个淬灭的奇异夸克来补充FK来设定标度,则对应于[^ \MSbar(2 GeV)]^(1/3)=263(3)(4)MeV和F=85.8(7)(20)MeV。

英文摘要:

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of (Mpi^2 Fpi^2)/2 with respect to the quark mass m in the chiral limit, where Mpi and Fpi are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use CLS lattices at three values of the lattice spacing in the range 0.05-0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks-Casher mechanism, and the rate of condensation agrees with the Gell-Mann-Oakes-Renner (GMOR) relation. For the renormalisation-group-invariant ratios we obtain [Σ^RGI]^(1/3)/F =2.77(2)(4) and Lambda^MSbar/F = 3.6(2), which correspond to [Σ^\MSbar(2 GeV)]^(1/3) =263(3)(4) MeV and F=85.8(7)(20) MeV if FK is used to set the scale by supplementing the theory with a quenched strange quark.

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