Perturbative Renormalizability of Chiral Two Pion Exchange and Power Counting in Nucleon-Nucleon Scattering

TL;DR

This paper demonstrates a method to renormalize chiral two pion exchange perturbatively in nucleon-nucleon scattering, addressing inconsistencies in Weinberg's counting and proposing modifications to power counting schemes.

Contribution

It introduces a perturbative renormalization approach for chiral two pion exchange, aligning with Nogga, Timmermans, and van Kolck's counting proposal, and explores power counting modifications in the singlet channel.

Findings

Perturbative treatment avoids inconsistencies in Weinberg's counting.

Renormalization leads to modified power counting schemes.

Applicable to nucleon-nucleon scattering in the singlet channel.

Abstract

We show how to renormalize chiral two pion exchange perturbatively if one pion exchange has already been fully iterated at leading order. This particular choice corresponds to the implementation of the counting proposal of Nogga, Timmermans and van Kolck at subleading orders. We illustrate why the perturbative treatment of the two pion exchange contributions is mandatory in order to avoid certain inconsistencies in Weinberg's counting. In addition, renormalizability implies modifications of the power counting which we explore for the particular case of the singlet channel.