Determining some pseudoscalar meson masses from axial anomaly

Following our previous work [C. Y. Liu, Mod. Phys. Lett. A 36, 2150080 (2021), doi:10.1142/S0217732321500802], we investigate the masses of some pseudoscalar mesons which have the anomalous decays from axial anomaly (the Adler-Bell-Jackiw anomaly). We apply a non-perturbative mass formula to study the neutral single flavor pseudoscalar meson (f (f) over bar). We find the mass of pseudoscalar meson (c (c) over bar) (m((c (c) over bar)) approximate to 7.6 GeV) which can solve the problem of double cc production in e(+)e(-) annihilation at root s approximate to 10.6 GeV and obtain the mass of pseudoscalar meson (b (b) over bar) (m((b (b) over bar)) approximate to 28.4 GeV) which is the same as the invariant mass of mu(+)mu(-) pairs produced in association with b jet in pp-collisions at the LHC. We generalize this formula to three flavors pseudoscalar mesons, we obtain the mass of eta' meson (m(eta') approximate to 961 MeV) which is almost the same as the experimental value (m(eta')(exp) approximate to 958 MeV).