$η$和$η^{\prime}$介子的性质：质量、衰变常数和胶子矩阵元
Properties of the $η$ and $η^{\prime}$ mesons: Masses, decay constants and gluonic matrix elements
摘要：
我们给出了$η$和$η^\prime$的质量和它们在物理点的四个独立衰变常数以及它们的反常胶子矩阵元$a_{η^{(\prime)}}$的结果。对21个$N_f = 2+1$协调格子模拟（CLS）系综进行了手征和连续极限外推，其中包括一个非常接近物理夸克质量的系综，系综采用非微扰改进的Wilson费米子，在四种不同的晶格间距和夸克质量平面上沿两条轨迹运动.第一次直接从轴向矢量矩阵元素确定衰减常数，而无需模型假设。这使我们能够研究它们的QCD标度依赖性，并确定所有的低能常数，有助于在下一个领先的顺序在大$N_c$ ChPT在一个定义良好的QCD重整化标度。我们还讨论了高激发态的$1400\,\mathrm{MeV}$区域。
英文摘要：
We present results for the $η$ and $η^\prime$ masses and their four independent decay constants at the physical point as well as their anomalous gluonic matrix elements $a_{η^{(\prime)}}$. The chiral and continuum limit extrapolation is performed on twenty-one $N_f = 2+1$ Coordinated Lattice Simulations (CLS) ensembles with non-perturbatively improved Wilson fermions at four different lattice spacings and along two trajectories in the quark mass plane, including one ensemble very close to physical quark masses. For the first time the decay constants are determined directly from the axialvector matrix elements without model assumptions. This allows us to study their QCD scale dependence and to determine all low-energy constants contributing at next-to-leading order in large-$N_c$ ChPT at a well defined QCD renormalization scale. We also discuss higher excited states in the $1400\,\mathrm{MeV}$ region.
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