Nonfactorization of four-quark condensates at low energies within chiral perturbation theory

Abstract

Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within chiral perturbation theory. We define the four-quark condensate as lim(x -> 0) < T((q) over barq)(x)((q) over barq)(0)>, which is equivalent to other definitions commonly used in the literature. Factorization of the four-quark condensate holds to leading and next to leading order. However, at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a nonfactorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large N-c limit, provided such a limit is taken before renormalization.