Effects of flavour-dependent q(q)over-bar annihilation on the mixing angleof the isoscalar octet-singlet and Schwinger's nonet mass formula

By incorporating the flavour-dependent quark-antiquark annihilation amplitu de into the mass-squared matrix describing the mixing of the isoscalar stat es of a meson nonet, the new version of Schwinger's nonet mass formula, whi ch 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 degrees, which is in agreement with the value range from -13 degree s to -17 degrees deduced from a rather exhaustive and up-to-date analysis o f data. It is also pointed out that the omission of the flavour-dependent q (q) over bar annihilation effect might be a factor resulting in the invali dity of Schwinger's original nonet mass formula for the pseudoscalar nonet.