Renormalizing Chiral Nuclear Forces: A Case Study of 3P0

TL;DR

This paper examines the renormalization of subleading contact interactions in the 3P0 nucleon-nucleon scattering channel, revealing limitations of Weinberg's power counting and proposing a modified approach aligned with renormalization group invariance.

Contribution

It demonstrates that Weinberg's original power counting fails at subleading orders in 3P0 and proposes a modified naive dimensional analysis for correct counterterm structure.

Findings

Weinberg's power counting does not ensure renormalization group invariance at subleading order.

Counterterm structure aligns with a modified naive dimensional analysis.

Identifies cutoff ranges where subleading potentials can be iterated with leading ones.

Abstract

We discuss in this paper the subleading contact interactions, or counterterms, in the 3P0 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 investigate whether 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 3P0 as an example, we also study the cutoffs where the subleading potential can be iterated together with the leading one.