Deconstructing triplet nucleon-nucleon scattering

TL;DR

This paper analyzes nucleon-nucleon scattering in spin-triplet channels using an effective field theory with nonperturbative one-pion exchange, revealing a new power counting scheme that improves understanding of short-range interactions.

Contribution

It introduces a modified power counting approach for nucleon-nucleon interactions that accounts for the singular tensor potential and identifies energy regimes where different counting schemes apply.

Findings

Residual scattering in low angular momentum waves is well described by the new counting.

High angular momentum waves follow perturbative counting up to 300 MeV.

A critical momentum distinguishes regimes where the new or perturbative counting is valid.

Abstract

Nucleon-nucleon scattering in spin-triplet channels is analysed within an effective field theory where one-pion exchange is treated nonperturbatively. Justifying this requires the identification of an additional low-energy scale in the strength of that potential. Short-range interactions are organised according to the resulting power counting, in which the leading term is promoted to significantly lower order than in the usual perturbative counting. In each channel there is a critical momentum above which the waves probe the singular core of the tensor potential and the new counting is necessary. When the effects of one- and two-pion exchange have been removed using a distorted-wave Born approximation, the residual scattering in waves with L<=2 is well described by the first three terms in the new counting. In contrast, the scattering in waves with L>=3 is consistent with the perturbative counting, at least for energies up to 300 MeV. This pattern is in agreement with estimates of the critical momenta in these channels.