The slope of the U(1) topological charge from gluonia sum rules and higher order effects on the pseudoscalar meson masses and mixing angles

Abstract

We reconsider the estimate of the slope of the U(1) topological charge from gluonia sum rules and we find ψ′(0)=−(7±3 MeV) 2. Then, including the pseudoscalar gluonium and loop corrections from the high dimension terms in the effective lagrangian, we reconsider the masses and mixings of the pseudoscalar mesons at the meson poles. The observed masses of the η and η′ mesons fix the values of the coupling constants of the effective lagrangian. A best fit of these masses fixes the values of the η−η′ and η′−ι mixing angles. The former is less accurate and is around −(23°–32°) while we find for the later θ η− ι ≅10°– 11°.