Revisiting the pseudoscalar meson and glueball mixing and key issues in the search for pseudscalar glueball state

Abstract

We revisit the mixing mechanism for pesudscalar mesons and glueball which is introduced by the axial vector anomaly. We demonstrate that the physical mass of the pseudoscalar glueball does not favor to be lower than 1.8 GeV if all the parameters are reasonably constrained. This conclusion, on the one hand, can accommodate the pseudoscalar glueball mass calculated by Lattice QCD, and on the other hand, is consistent with the high-statistics analyses at BESIII that all the available measurements do not support the presence of two closely overlapping pseudoscalar states in any exclusive channel. Such a result is in agreement with the recent claim that the slightly shifted peak positions for two possible states $\eta (1405)$ and $\eta (1475)$ observed in different channels are actually originated from one single state with the triangle singularity interferences. By resolving this long-standing paradox, one should pay more attention to higher mass region for the purpose of searching for the pseudoscalar glueball candidate.

17 pages, 5 figures; Revised version accepted by Phys. Rev. D

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Cited by in corpus (12)

• An updated review of the new hadron states
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• Study of the pseudoscalar glueball in $J/\psi$ radiative decays
• Internal particle width effects on the the triangle singularity mechanism in the study of the $\eta (1405)$ and $\eta (1475)$ puzzle
• Considerations on the Schmid theorem for triangle singularities
• Dispersive analysis of glueball masses
• The Glueball content of ${\eta }_c$
• QCD sum rule studies on the $ss\bar{s}\bar{s}$ tetraquark states of $J^{PC}=0^{-+}$
• New puzzle in charmonium decays
• $\eta$-glueball mixing from $N_f=2$ lattice QCD
• Dispersive analysis of excited glueball states
• Nature of $X(2370)$