Non-factorization 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. 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. We also comment on how factorization still holds in the large $N_c$ limit, provided such a limit is taken before renormalization.

12 pages, one figure, version accepted in Phys. Rev. D. New appendix with technical details and further comments and references added throughout the text

References in corpus (4)

• Chiral Perturbation Theory Beyond One Loop
• Integrating out strange quarks in ChPT
• Integrating out strange quarks in ChPT: terms at order p^6
• General formula for the four-quark condensate and vacuum factorization assumption

Cited by in corpus (4)

• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• Factorization breaking of four-quark condensates in the Nambu Jona Lasinio model
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Temperature dependence of Quark and Gluon condensate In The Dyson-Schwinger Equations At Finite Temperature