Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering

TL;DR

This paper investigates the conditions under which chiral two pion exchange in nucleon-nucleon scattering can be treated perturbatively within effective field theory, identifying the necessary counterterms and momentum ranges for validity.

Contribution

It demonstrates the perturbative renormalizability of chiral two pion exchange with specific counterterms for different channels and establishes the applicable momentum ranges.

Findings

Three counterterms needed for singlet channel

Six counterterms needed for triplet channel

Perturbative treatment valid up to 200-300 MeV (singlet) and 300-400 MeV (triplet)

Abstract

We study the perturbative renormalizability of chiral two pion exchange for the singlet and triplet channels within effective field theory, provided that the one pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed in order to obtain finite results when the cut-off is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that chiral two pion exchange can be treated perturbatively up to a center-of-mass momentum of k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in the triplet.