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We revisit the mixing mechanism for pesudscalar mesons and glueball which isintroduced by the axial vector anomaly. We demonstrate that the physical massof the pseudoscalar glueball does not favor to be lower than 1.8 GeV if all theparameters are reasonably constrained. This conclusion, on the one hand, canaccommodate the pseudoscalar glueball mass calculated by Lattice QCD, and onthe other hand, is consistent with the high-statistics analyses at BESIII thatall the available measurements do not support the presence of two closelyoverlapping pseudoscalar states in any exclusive channel. Such a result is inagreement with the recent claim that the slightly shifted peak positions fortwo possible states $\eta(1405)$ and $\eta(1475)$ observed in differentchannels are actually originated from one single state with the trianglesingularity interferences. By resolving this long-standing paradox, one shouldpay more attention to higher mass region for the purpose of searching for thepseudoscalar glueball candidate.

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