Self-mass for Massive Quark

We study the behavior of the self-mass for a quark with a current mass larger than $\Lambda_QCD$, as a function of its Euclidean momentum and mass, in QCD. An expression for the Bethe-Salpeter kernel of the Schwinger-Dyson (SD) equation valid in both the infrared and ultraviolet regions is obtained based on a renormalization group analysis. The resulting SD equation is solved numerically. It is found that the quark constituent mass at zero momentum is substantially enhanced due to its effective gauge interaction. The solution in the ultraviolet region agrees well with the known asymptotic solution. The self-mass scales exactly as the on-shell current mass at a fixed momentum.