Pseudoscalar glueball in a chiral Lagrangian model with instanton effect

Abstract

We study the pseudoscalar glueball ground state in a chiral effective Lagrangian model proposed by 't Hooft, motivated by taking into account the instanton effects, which can describe not only the chiral symmetry breaking, but also the solution of ${U}_{A}(1)$. We study the parameter space allowed by constraints from vacuum conditions and unitary bounds. By considering two scenarios in the ${0}^{++}$ sector, we find that parameter space which can accommodate the ${0}^{\ensuremath{-}+}$ sector is sensitive to the conditions in ${0}^{++}$ sector. From our analysis, it is found that three $\ensuremath{\eta}$ states, i.e. $\ensuremath{\eta}(1295)$, $\ensuremath{\eta}(1405)$, $\ensuremath{\eta}(1475)$, can be the pseudoscalar glueball ground state if we assume that the lightest ${0}^{++}$ glueball ground state has a mass 1710 (or 1500) MeV. While there will be no ${0}^{\ensuremath{-}+}$ glueball candidate ground state found in experiments if we assume that the lightest ${0}^{++}$ glueball ground state has a mass 660 MeV. We also point out the determined instanton density (i.e. the parameter ${k}_{t}$) is consistent with those determined from other methods, e.g. instanton liquid approximation and lattice simulations.