Pseudoscalar glueball and ${\eta }^{\mathrm{\prime }}$-meson in low-energy QCD expansion

An effective chiral lagrangian of order $p^2$, describing the interaction of light pseudoscalar (PS) mesons with ${\eta }^{\mathrm{\prime }}$-meson and PS-glueball, has been determined taking into consideration the renorm-group requirements imposed by QCD renormalization. It is shown that the interpolating fields for the lowest singlet quarkic and gluonic states, ${\eta }^0$ and ${\eta }^G$, may be involved into the effective theory to be renorm-invariant objects not mixing due to QCD renormalization. It is established that the potential describing the mass'' term of the lagrangian does not depend on $\eta^0$. The dependence on $\eta^G$ is permitted only when there is not direct interaction between $\eta^0$ and $\eta^G$ out of the mass’’ term without the octet fields contribution. The peculiarities distinguishing the glueball from excitation over ${\eta }^0$ have been considered.