Perturbative $NN$ scattering in chiral effective field theory

TL;DR

This paper investigates the applicability of perturbative methods in chiral effective field theory for nucleon-nucleon scattering, identifying which partial waves can be treated perturbatively and demonstrating good agreement with empirical data up to 300 MeV.

Contribution

It determines the lowest angular momenta where perturbative treatment of chiral forces is valid and shows perturbation theory's effectiveness in describing certain partial waves.

Findings

Perturbation theory applies to all partial waves except ${}^1S_0$, ${}^3S_1 - {}^3D_1$, and ${}^3P_0$.

Good agreement with empirical phase shifts up to 300 MeV for applicable waves.

Perturbative approach is viable in chiral EFT for specific nucleon-nucleon partial waves.

Abstract

Within the framework of chiral effective field theory, perturbative calculation for $NN$ scattering is carried out in partial waves with orbital angular momentum $L \geqslant 1$. The primary goal is to identify the lowest angular momenta at which perturbative treatment of chiral forces can apply. Results up to the order where the subleading two-pion exchange appears are shown. It is concluded that perturbation theory applies to all partial waves but ${}^1S_0$, ${}^3S_1 - {}^3D_1$, and ${}^3P_0$. Where it is applicable, perturbation theory with the delta-less chiral forces produces good agreement with the empirical phase shifts up to $k_\text{c.m.} \simeq 300$ MeV.