Dynamical symmetry breaking, confinement with flat-bottom potential

In this article, we calculate the dressed quark propagator with the flat bottom potential in the framework of the rain-bow Schwinger-Dyson equation. Then based on the nonperturbative dressed quark propagator, we calculate the $π$ decay constant and the quark condensate. The $π$ decay constant is an important parameter in describing the interplay between dynamical symmetry breaking and confinement, while the quark condensate is an order parameter for dynamical chiral symmetry breaking. To implement confinement, we prove that the dressed quark propagator has no poles on the real timelike $p^2$ axial, the absence of Kallen-Lehmann spectral representation obviously precludes the existence of free quarks.

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