Four-Quark States and Nucleon-Antinucleon Annihilation within the Quark Model with Instanton Induced Interaction

The spectrum of $q^2\bar q^2, J^p=0^+,2^+$ mesons is discussed. We have shown that due to instanton - induced forces the physical states are strong mixtures of the $SU_f(3)$ group basis states. The cross-sections for annihilation of the $N\bar N$ system into $(q^2\bar q^2)(q\bar q)$ mesons are obtained. The $a_0(980)$ meson is considered as $q^2\bar q^2$ meson consisting of $9_f$ and $36_f$ plets. The branchings are also predicted for the cross-sections for production of the $a_0(980)$ and tensor $q^2\bar q^2$ mesons in $N\bar N$ annihilation.