Pseudoscalar glueball and $η'$-meson in low-energy QCD expansion

Abstract

An effective chiral lagrangian of order $p^2$, describing the interaction of light pseudoscalar (PS) mesons with $η'$-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, $η^0$ and $η^G$, 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 $η^0$. The dependence on $η^G$ is permitted only when there is not direct interaction between $η^0$ and $η^G$ out of the ``mass'' term without the octet fields contribution. The peculiarities distinguishing the glueball from excitation over $η^0$ have been considered.