Schwinger-Dyson equation in QCD: Comparison of some approximations

Systematic improvements to approximating the ladder Schwinger-Dyson equation in QCD are presented. Improvements considered are the inclusion of higher-order terms in an expansion of the angular integration in the kernel and the inclusion of two-loop terms in the gluon propagator. It is stressed that the latter are necessary when considering the subleading asymptotic behavior of the solutions. Simple means of guaranteeing the correct derivatives at the origin are presented. A compact approximation is given with correct first and second derivatives at the origin and with asymptotic behavior in agreement with operator-product-expansion analysis. The expression for the two-loop asymptotic irregular solution is derived and compared with the renormalization-group result. The expression for the two-loop asymptotic regular solution is also calculated.