Effects of Flavour-Dependent qq Annihilation on the Mixing Angle of the Isoscalar Octet--Singlet and Schwinger’s Nonet Mass Formula

By incorporating the flavour-dependent quark--antiquark annihilation amplitude into the mass-squared matrix describing the mixing of the isoscalar states of a meson nonet, the new version of Schwinger's nonet mass formula, which holds with a high accuracy for the 0^-+, 1^--, 2⁺⁺, 2^-+ and 3^-- nonets, is derived and the mixing angle of the isoscalar octet--singlet for these nonets is obtained. In particular, the mixing angle of the isoscalar octet--singlet for the pseudoscalar nonet is determined to take the value of -12.92°, which is in agreement with the value range from -13° to -17° deduced from a rather exhaustive and up-to-date analysis of data. It is also pointed out that the omission of the flavour-dependent qq annihilation effect might be a factor resulting in the invalidity of Schwinger’s original nonet mass formula for the pseudoscalar nonet.