Renormalizing chiral nuclear forces: A case study of 3P0

We discuss in this Brief Report the subleading contact interactions, or counterterms, in the P-3(0) channel of nucleon-nucleon scattering up to O(Q(3)), where, already at leading order, Weinberg's original power counting (WPC) scheme fails to fulfill renormalization group invariance due to the singular attraction of one-pion exchange. Treating the subleading interactions as perturbations and using renormalization group invariance as the criterion, we investigatewhether WPC, although missing the leading order, could prescribe correct subleading counterterms. We find that the answer is negative and, instead, that the structure of counterterms agrees with a modified version of naive dimensional analysis. Using P-3(0) as an example, we also study the cutoffs where the subleading potential can be iterated together with the leading one.