$\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ 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 $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ masses and also the mixing angle to be $m_{\hat{I}}\cdot =0.505(72)(75)$ GeV, $m_{\hat{I}{\cdot }^{\prime }}=0.952(47)(40)$ GeV, and $\hat{I}{¸}_1=-8.9(2.1)(1.8{)}^{\circ }$, respectively, where the first error is the statistical uncertainty and the second one is the systematic uncertainty. This is the first extraction of both $\hat{I}\cdot /\hat{I}{\cdot }^{\prime }$ masses and the mixing angle $\hat{I}{¸}_1$ using topological charge operators. Compared with previous studies using quark bilinear operators, the error of the $\hat{I}\cdot$ mass is relatively large, but the mixing angle has comparable precision. This demonstrates that the topological charge operators are well suited to study the $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ mesons.

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