Spectral-Function Sum Rules with Symmetry Breaking

The symmetry breaking based on Okubo's ansatz is considered to modify Weinberg's spectral-function sum rules (particularly the second). We then apply the modified sum rules to the chiral $U\left(3\right)\mathrm{}\times U\left(3\right)\mathrm{}$ and obtain physically interesting results for the mass relation and mixing angles of the vector mesons, a nonet assignment of the axial-vector mesons, and the decay constants of the pseudoscalar mesons.