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

Understand

Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within Chiral Perturbation Theory.

• 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 non-factorization term vanishes only in the chiral limit.