We present two things in this discussion. First, we develop and prove the theory of the extension of the YFS Monte Carlo approach to higher order SU_2L\times U₁ radiative corrections to the analogous higher order QCD radiative corrections. Contact is made with other pioneering soft gluon resummation theories in the literature. Second, semi-analytical results and preliminary explicit Monte Carlo data are presented for the specific example of the processes p\bar{p}\rightarrow t\bar {t}+n(G)+X at FNAL energies, where G is a soft gluon and the respective event generator, ttp1.0, features realistic, event-by-event simulation of multiple, soft, finite p_T gluon effects in which the infrared singularities are canceled to all orders in \alpha_s. We comment briefly on the implications of our results on the CDF/D0 observations and on their possible applications to RHIC physics and to LHC physics.

PACS numbers: 02.70.Uu, 12.38.Cy