Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space

The renormalization of the chiral np interaction in the 1S0 channel to N3LO in Weinberg counting for the long distance potential with one single momentum and energy independent counterterm is carried out. This renormalization scheme yields finite and unique results and is free of short distance off-shell ambiguities. We observe good convergence in the entire elastic range below pion production threshold and find that there are some small physical effects missing in the purely pionic chiral NN potential with or without inclusion of explicit Delta degrees of freedom. We also study the renormalizability of the standard Weinberg counting at NLO and N2LO when a momentum dependent polynomial counterterm is included. Our numerical results suggest that the inclusion of this counterterm does not yield a convergent amplitude (at NLO and N2LO).