Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System

TL;DR

This paper investigates the renormalization of higher partial waves in antinucleon-nucleon scattering within chiral effective field theory, emphasizing the role of contact interactions and cutoff dependence in ensuring consistent phase shift predictions.

Contribution

It extends previous work by analyzing higher partial waves with total angular momentum up to J=3, demonstrating the necessity of contact interactions at leading order for certain channels.

Findings

Contact interactions are essential in channels with attractive tensor potentials.

Cutoff dependence affects phase shifts, inelasticities, and mixing angles.

Results align with partial-wave analysis data.

Abstract

The renormalization of iterated one-pion exchange (OPE) has been studied in Chiral Effective Field Theory ($\chi$EFT) for the antinucleon-nucleon ($\overline{N}\!N$) scattering in some partial waves (Phys. Rev. C 105, 054005 (2022)). We go further for the other higher partial waves but with total angular momenta $J\leq 3$ in this paper. Contact interactions are represented by a complex spherical well in coordinate space. Changing the radius of the spherical well means changing the cutoff. We check the cutoff dependence of the phase shifts, inelasticities, and mixing angles for the partial waves, and show that contact interactions are needed at leading order in channels where the singular tensor potentials of OPE are attractive. Results are compared with the energy-dependent partial-wave analysis of $\overline{N}\!N$ scattering data. Comparisons between our conclusions and applications of $\chi$EFT to the nucleon-nucleon system are discussed as well.