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arXiv · 2205.12541

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

Xiangyu Jiang·Wei Sun·Feiyu Chen·Ying Chen·Ming Gong·Zhaofeng Liu·Renqiang Zhang
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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 $\mathrm{U_A(1)}$ anomaly.

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Xiangyu Jiang, Wei Sun, Feiyu Chen, Ying Chen, Ming Gong, Zhaofeng Liu, Renqiang Zhang. 2022-05-25. $\eta$-glueball mixing from $N_f=2$ lattice QCD. https://doi.org/10.1103/physrevd.107.094510

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