General formula for the four-quark condensate and vacuum factorization assumption

Details General formula for the four-quark condensate and vacuum factorization assumption General formula for the four-quark condensate and vacuum factorization assumption

2006-09-12

arxiv.org/abs/hep-ph/0609108v1

Int.J.Mod.Phys.A23:1507-1520,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

Revtex4, 11 pages, no figures

Scientific paper

10.1142/S0217751X08039700

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):|{\tilde 0}>$. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):| {\tilde 0}>$ holds only when the dressed vertex is taken to be the bare one. This property also holds for all other type of four-quark condensate.

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