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

Abstract

We investigate the factorization hypothesis of the four-quark condensate $⟨q\bar{q}q\bar{q}⟩=A⟨q\bar{q}{⟩}^2$ 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.

Comments: 10 pages, revised version, some corrected expressions