Model of broken chiral symmetry for of mesons

The method of small oscillations is used to obtain mass formulas for $0^\pm$-mesons in the framework of the $SU_3$ a sigma model. The general properties of the spectrum are considered from the point of view of the symmetry of the vacuum and of the Lagrangian. Expressions are also obtained for the divergences of the vector and axial currents and a study is made of a realization of the $SU_3$- and $SU_3\otimes SU_3$ symmetries on the basis of a solution of the condition of vacuum stability.