Reexamining the perturbative renormalizability of the coupled triplets

Abstract

I reexamine the perturbative renormalizability of chiral two-pion exchange in two-nucleon scattering for coupled triplets when one-pion exchange has been fully iterated at leading order. Improving over previous works, it is shown that only two counterterms are required to obtain cutoff independent results, which is one less than in naive dimensional analysis. The explanation for this reduction is the existence of an attractive and repulsive eigenchannel in the one-pion exchange potential for the coupled triplets: the attractive eigenchannel can be renormalized like a regular attractive uncoupled triplet, while the repulsive eigenchannel is always finite regardless of whether there are counterterms or not. I discuss the implications of this finding for the power counting of the $^3S_1$-$^3D_1$ and $^3P_2$-$^3F_2$ partial waves.