We introduce novel relations between the derivatives [${\partial }^n\rho (\lambda ,m_l)/\partial m_l^n$] of the Dirac eigenvalue spectrum [$\rho (\lambda ,m_l)$] with respect to the light sea quark mass ($m_l$) and the ($n+1$)-point correlations among the eigenvalues ($\lambda$) of the massless Dirac operator. Using these relations we present lattice QCD results for ${\partial }^n\rho (\lambda ,m_l)/\partial m_l^n$ ($n=1$, 2, 3) for $m_l$ corresponding to pion masses $m_{\pi }=160–55\mathrm{MeV}$ and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using ($2+1$) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings $a=0.12$, 0.08, 0.06 fm, and lattices having aspect ratios 4–9. We find that $\rho (\lambda \to 0,m_l)$ develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as $a\to 0$, and its amplitude is proportional to $m_l^2$. We demonstrate that this $\rho (\lambda \to 0,m_l)$ is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

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相关的狄拉克特征值和手性对称QCD的轴异常

我们介绍衍生物之间的新颖关系[${\partial }^{ñ}\rho （\lambda ，{米}_{升}）/\partial {米}_{升}^{ñ}$Dirac特征值谱[$\rho （\lambda ，{米}_{升}）$]关于轻海夸克质量（${米}_{升}$）和（$ñ+\mathrm{1个}$特征值之间的点相关$\lambda$）的质量Dirac运算符。利用这些关系，我们为${\partial }^{ñ}\rho （\lambda ，{米}_{升}）/\partial {米}_{升}^{ñ}$ （$ñ=\mathrm{1个}$，2，3）为 ${米}_{升}$ 对应于介子质量 ${米}_{\pi }=160–55\mathrm{病毒}$且温度约为手性相变温度的1.6倍。使用（$2+\mathrm{1个}$）高度改良的交错夸克的味道，具有奇怪的夸克质量，三个晶格间距的物理值 $\mathrm{一种}=0.12$，0.08、0.06 fm和长宽比为4–9的晶格。我们发现$\rho （\lambda \to 0，{米}_{升}）$形成尖峰结构。这种峰形结构是由于狄拉克特征值光谱的红外部分内的非泊松相关而产生的，随着$\mathrm{一种}\to 0$，其幅度与 ${米}_{升}^2$。我们证明了这一点$\rho （\lambda \to 0，{米}_{升}）$负责光标量子和伪标量子介子的两点相关函数中的轴向异常的表现。在进行连续谱和手性外推后，我们发现轴向异常仍然表现在手性极限内标量介子和伪标介子的两点相关函数中。