Nonperturbative renormalization of the chiral nucleon-nucleon interaction up to next-to-next-to-leading order

We study the nonperturbative renormalization of the nucleon-nucleon ($NN$) interaction at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) of chiral effective field theory. A systematic variation of the cutoff parameter is performed for values below the chiral symmetry breaking scale of about 1 GeV. The accuracy of the predictions is determined by calculating the $\chi^2$ for the reproduction of the $NN$ data for energy intervals below pion-production threshold. At NLO, $NN$ data are described well up to about 100 MeV laboratory energy and, at NNLO, up to about 200 MeV---with, essentially, cutoff independence for cutoffs between about 450 and 850 MeV.