Mixing Angles and Decay Constants in the SU(4) Mixing Scheme of η–η′–ηc–ι

Abstract

We extend the SU(3) mixing of isosinglet pseudoscalar mesons to the SU(4) level with η, η′, ηc and ι. The quarkonium gluonium content of the physical states at the SU(4) level are being numerically estimated. We derive a mass relation at the SU(4) level taking the divergence of vector current into account and solve for the SU(4) mixing angles and decay constants using the constraints obtained from anomalous Ward identities, the mass relation, topological susceptibility, SU(4) transformation properties of pseudoscalar density, experimental data and other presently available constraints. The mixing has suggested that besides charm quark content, ηc meson has some percentage of normal and strange quarks along with gluonium as its constituents.