  Naively, the "best" method of renormalization is the one where a momentum
cutoff is taken to infinity while maintaining stable results due to a
cutoff-dependent adjustment of counterterms. We have applied this
renormalization method in the non-perturbative calculation of phase-shifts for
nucleon-nucleon (NN) scattering using chiral NN potentials up to
next-to-next-to-next-to-leading order (N3LO). For lower partial waves, we find
that there is either no convergence with increasing order or, if convergence
occurs, the results do not always converge to the empirical values. For higher
partial waves, we always observe convergence to the empirical phase shifts
(except for the 3G5 state). Furthermore, no matter what the order is, one can
use only one or no counterterm per partial wave, creating a rather erratic
scheme of power counting that does not allow for a systematic order-by-order
improvement of the predictions. The conclusion is that infinite-cutoff
renormalization is inappropriate for chiral NN interactions, which should not
come as a surprise, since the chiral effective field theory, these interactions
are based upon, is designed for momenta below the chiral-symmetry breaking
scale of about 1 GeV. Therefore, this value for the hard scale should also be
perceived as the appropriate upper limit for the momentum cutoff.
