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.