Renormalizing Chiral Nuclear Forces: Triplet Channels

TL;DR

This paper analyzes the renormalization of chiral nuclear forces in triplet channels, proposing a modified power counting scheme that accounts for singular attractions and ensures renormalization group invariance.

Contribution

It introduces a modified power counting approach for triplet channels in chiral effective field theory, refining Weinberg's original scheme based on renormalization group considerations.

Findings

WPC remains valid for 3S1-3D1 and 3P1 channels.

A two-order enhancement is required for 3P0 and 3P2-3F2 channels.

The modified scheme ensures consistent renormalization across triplet channels.

Abstract

We discuss the subleading contact interactions, or counterterms, of the triplet channels of nucleon-nucleon scattering in the framework of chiral effective field theory, with S and P waves as the examples. The triplet channels are special in that they allow the singular attraction of one-pion exchange to modify Weinberg's original power counting (WPC) scheme. With renormalization group invariance as the constraint, our power counting for the triplet channels can be summarized as a modified version of naive dimensional analysis in which, when compared with WPC, all of the counterterms in a given partial wave (leading or subleading) are enhanced by the same amount. More specifically, this means that WPC needs no modification in 3S1-3D1 and 3P1, whereas a two-order enhancement is necessary in both 3P0 and 3P2 - 3F2.