The Effect of Retardation on the Spontaneous Breaking of Chiral Symmetry in GCM

Abstract

An effective Hamiltonian including current-current coupling from the Global Color symmetry Model (GCM) is derived. Retardation effects are introduced by the factor R √ π e −R 2 τ 2 , instead of δ(τ) in the correlation kernel, from which the retardation gap equation with α − α coupling in the 3 P 0 vacuum is obtained. qq condensation of different retardation parameters R with or without the α − α term are calculated. The results show the effects of retardation, and indicate that the typical value of R is about 2 f m −1 at reasonable value ofqq condensation. And while taking typical value 1 fm −1 of R, the condensation qq 1 3 is about 13% larger than that with no retardation effect. With the α − α terms, the condensation qq 1 3 are about 17% larger than that without it for all values of the parameter R. This shows the retardation effects and the α − α terms are important for further studying in low region.