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

Abstract

An effective chiral lagrangian of order $p^2$, describing the interaction of light pseudoscalar (PS) mesons with ${\eta }^{\prime }$-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.

Comments: 16 pages, LaTeX, no figures. Erratum in signs in Eqs. (18), (A.5) and (A.6)