Gell-Mann-Low style renormalization group methods are employed in conjunction with dimensional regularizations and ∊ expansions to study the bead-spring model of polymers with excluded volume in dilute solutions. Perturbation calculations are carried out through order ∊2 for the translational diffusion coefficient D (∊=4-d, d being the spatial dimension) both with and without the use of the preaveraging approximation. Polymer excluded volume interactions are systematically incorporated into the Rouse-Zimm model by using the well-known two parameter model along with the ∊ expansion. The nondraining limit hydrodynamic interaction fixed point is found to be unaffected by preaveraging through order ∊2 and is identical to that obtained previously from the order ∊2 preaveraged Kirkwood-Riseman formalism. Our work indicates that the nonpreaveraged renormalization group perturbation expansions appear more well behaved (controllable) in the Rouse-Zimm model than in the Kirkwood-Riseman rigid body model.