$\eta$-glueball mixing from $N_f=2$ lattice QCD

Abstract

We perform the first lattice study on the mixing of the isoscalar pseudoscalar meson $\eta$ and the pseudoscalar glueball $G$ in the $N_f=2$ QCD at the pion mass $m_{\pi }\approx 350$ MeV. The $\eta$ mass is determined to be $m_{\eta }=714(6)(16)$ MeV. Through the Witten-Veneziano relation, this value can be matched to a mass value of $\sim 981$ MeV for the $\mathrm{SU}(3)$ counterpart of $\eta$. Based on a large gauge ensemble, the $\eta -G$ mixing energy and the mixing angle are determined to be $|x|=107(15)(2)$ MeV and $|\theta |=3.46(46{)}^{\circ }$ from the $\eta -G$ correlators that are calculated using the distillation method. We conclude that the $\eta -G$ mixing is tiny and the topology induced interaction contributes most of $\eta$ mass owing to the QCD ${\mathrm{U}}_{\mathrm{A}}(1)$ anomaly.

Comments: 13 pages, 12 figures