Dipartimento di Fisica, Università di Milano-Bicocca, and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy.
John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, D-15738 Zeuthen, Germany.
Phys Rev Lett. 2015 Mar 20;114(11):112001. doi: 10.1103/PhysRevLett.114.112001. Epub 2015 Mar 16.
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 M(π)(2)F(π)(2)/2 with respect to the quark mass m in the chiral limit, where M(π) and F(π) 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 lattices generated by the Coordinated Lattice Simulation (CLS) group 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 relation. For the renormalization-group-invariant ratios we obtain Σ(RGI)/F=2.77(2)(4) and Λ(M̅S)/F=3.6(2), which correspond to Σ(M̅S)(2 GeV)=263(3)(4) MeV and F=85.8(7)(20) MeV if F(K) is used to set the scale by supplementing the theory with a quenched strange quark.
QCD 中自发手征对称性破缺的一个显著特征是狄拉克算子低模在原点附近的凝聚。凝聚的速率必须等于手征极限下 M(π)(2)F(π)(2)/2 相对于夸克质量 m 的斜率，其中 M(π)和 F(π)是 Nambu-Goldstone 玻色子的质量和衰变常数。我们通过使用双轻简并 Wilson 夸克的格点 QCD 数值模拟来计算狄拉克算子、夸克质量、赝标介子质量和衰变常数的谱密度。我们使用 Coordinated Lattice Simulation (CLS) 小组生成的格点，在 0.05-0.08 fm 的格点间距范围内有三个值，并且对于几个夸克质量，对应于赝标介子质量低至 190 MeV。由于这个参数空间的覆盖，我们可以有信心地将所有量外推到手征和连续极限。结果表明，正如 Banks-Casher 机制所预期的那样，低夸克模式在连续相中确实凝聚了，凝聚的速率与 Gell-Mann-Oakes-Renner 关系一致。对于重整化群不变比，我们得到Σ(RGI)/F=2.77(2)(4)和 Λ(M̅S)/F=3.6(2)，如果用 quenched strange quark 补充理论并用 F(K)设置标度，则对应于Σ(M̅S)(2 GeV)=263(3)(4) MeV 和 F=85.8(7)(20) MeV。
