Pseudoscalar glueball and $η'$-meson in low-energy QCD expansion
Abstract
Description
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.
16 pages, LaTeX, no figures. Erratum in signs in Eqs. (18), (A.5) and (A.6)
16 pages, LaTeX, no figures. Erratum in signs in Eqs. (18), (A.5) and (A.6)