Study of the pseudoscalar glueball in $J/\psi$ radiative decays

Abstract

We aim to explore the production rate of the pseudoscalar glueball in $J/\psi$ radiative decay by lattice QCD in quenched approximation. The calculation is performed on three anisotropic lattices with the spatial lattice spacing ranging from 0.222(2) fm to 0.110(1) fm. As a calibration of some systematical uncertainties, we first extract the $M1$ form factor $\hat{V}(0)$ of the process $J/\psi \to \gamma {\eta }_c$ and get the result $\hat{V}(0)=1.933(41)$ in the continuum limit, which gives the partial width $\Gamma (J/\psi \to \gamma {\eta }_c)=2.47(11)$ keV. These results are in agreement with that of previous lattice studies. As for the pseudoscalar glueball $G_{0^{-+}}$, its mass is derived to be $2.395(14)$ GeV, and the form factor $\hat{V}(0)$ of the process $J/\psi \to \gamma G_{0^{-+}}$ is determined to be $\hat{V}(0)=0.0246(43)$ after continuum extrapolation. Finally, the production rate of the pseudoscalar glueball is predicted to be $2.31(90)\times 10^{-4}$, which is much smaller than that of conventional light $q\bar{q}$ $\eta$ states. After the subtraction of the phase space factor, the couplings of $J/\psi X\gamma$ are similar where $X$ stands for $\eta$ states and the pseudoscalar glueball. Possibly, the $U_A(1)$ anomaly plays an important role for the large couplings of gluons to the flavor singlet $\eta$ states in $J/\psi$ radiative decays.

arXiv comment11 pages, 16 figures, 7 tables, revised version. To appear in PRD

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• Lattice study of $J/\psi \to \gamma {\eta }_c$ using a method without momentum extrapolation
• The radiative decay of scalar glueball from lattice QCD
• Coupled-channel analysis of the near-threshold $e^{+}{e}^{-}\to N\bar{N}$ cross sections
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• The charmonium-like exotic hadron productions in $e^{+}{e}^{-}$ collisions at the BESIII energy with the PACIAE model
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$
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• A comparative lattice analysis of $SU(2)$ dark gluebal