Factorization breaking of four-quark condensates in the Nambu Jona Lasinio model

We investigate the factorization hypothesis of the four-quark condensate $langle q bar{q} q bar{q} rangle = , A , langle q bar{q} rangle^2$ with the help of the Nambu Jona-Lasinio Model supplemented with eighth order interactions. For that purpose we use the bosonization method with multiple auxiliary variables. We find that in a simplified U(1) version of the model factorization holds, whereas in the full SU(3)-flavor version of the model factorization is broken by terms which are related to the t Hooft interactions.