Publication: Nonfactorization of four-quark condensates at low energies within chiral perturbation theory
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2010-10-14
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Amer Physical Soc
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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.
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© 2010 The American Physical Society.
This work was partially supported by Spanish Ministerio de Educacion y Ciencia Research Contracts No. FPA2008-00592, No. FIS2006-03438, and No. FIS2008-01323, and by U.Complutense/Banco Santander Grant No. UCM-BSCH GR58/08 910309. We acknowledge the support of the European Community-Research Infrastructure Integrating Activity "Study of Strongly Interacting Matter" (acronym HadronPhysics2, Grant Agreement No. 227431) under the Seventh Framework Programme of the EU.
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