Isospin breaking in pion-deuteron scattering and the pion-nucleon scattering lengths

TL;DR

This paper reviews isospin-breaking effects in pion-nucleon and pion-deuteron scattering, emphasizing the cancellation of virtual-photon corrections and providing refined scattering length values from high-precision data.

Contribution

It offers a detailed analysis of electromagnetic correction mechanisms and defines pion-nucleon scattering lengths considering isospin-breaking effects, improving the interpretation of experimental data.

Findings

Virtual-photon corrections cancel in the pion-deuteron system.

Refined pion-nucleon scattering lengths are provided.

Analysis clarifies electromagnetic effects on scattering length definitions.

Abstract

In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon-nucleon scattering. Based on the pi^{+/-} p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a^{1/2}=(170.5 +/- 2.0) x 10^{-3} mpi^{-1} and a^{3/2}=(-86.5 +/- 1.8) x 10^{-3} mpi^{-1}.