$\eta$ and $\eta'$ 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 $\eta'$ masses and also the mixing angle to be $m_\eta = 0.505(72)(75)$ GeV, $m_{\eta'}=0.952(47)(40)$ 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 $\eta/\eta'$ 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 $\eta'$ mesons.