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Four-quark correlators and the factorization hypothesis are analyzed in themeson sector within Chiral Perturbation Theory. Factorization of the four-quarkcondensate holds to leading and next to leading order. However at next to nextto leading order, a term with a nontrivial space-time dependence in thefour-quark correlator yields a divergent four-quark condensate, whereas thetwo-quark condensate and the scalar susceptibility are finite. Such anon-factorization term vanishes only in the chiral limit. We also comment onhow factorization still holds in the large $N_c$ limit, provided such a limitis taken before renormalization.

Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory