$\eta$ and ${\eta }^{\prime }$ mesons from $N_f=2+1$ lattice QCD at the physical point using topological charge operators

Abstract

By fitting the two-point correlation functions of topological charge density operators calculated on two $2+1$-flavor gauge ensembles with physical pion mass, we determine both the $\eta$ and ${\eta }^{\prime }$ masses and also the mixing angle to be $m_{\eta }=0.505(72)(75)$ GeV, $m_{{\eta }^{\prime }}=0.952(47)(40)$ GeV, and ${\theta }_1=-8.9(2.1)(1.8{)}^{\circ }$, respectively, where the first error is the statistical uncertainty and the second one is the systematic uncertainty. This is the first extraction of both $\eta /{\eta }^{\prime }$ masses and the mixing angle ${\theta }_1$ using topological charge operators. Compared with previous studies using quark bilinear operators, the error of the $\eta$ mass is relatively large, but the mixing angle has comparable precision. This demonstrates that the topological charge operators are well suited to study the $\eta$ and ${\eta }^{\prime }$ mesons.

6 pages, 9 figures. Match the version accepted by PRD

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