A Rotated Skyrmion and Pions-Nucleon Interactions

TL;DR

This paper analyzes the asymptotic behavior of rotated skyrmions and their role in pion-nucleon interactions, demonstrating that classical pion fields contribute significantly to scattering amplitudes and reproduce known results.

Contribution

It introduces a detailed analysis of the rotated skyrmion's asymptotics in path integrals, showing classical pion fields' impact on pion-nucleon amplitudes, including Born diagrams.

Findings

Classical pion fields from rotated skyrmions contribute to scattering amplitudes.

The approach reproduces known pion-nucleon amplitudes with Born diagrams.

Asymptotic analysis confirms the radiational component of skyrmion solutions.

Abstract

It was shown by careful consideration of the time--dependent classic solution for the rotated skyrmion, that such solution at large distances has radiational component similar to the Lienart-Viehart retarded potential in Electrodynamics. We consider such solution as stationary phase configuration of the pion field in path integrals for the correlators of $n$ isovector axial currents $J_{\mu}^{A,i}$ and two nucleon currents $J_N$. $n$ pion -- nucleon amplitudes are extracted from these correlators. The careful account of the asymptotics of this stationary phase configuration of the pion field (rotated skyrmion) in path integral leads to nonzero contribution of this classical part of the total pion field to pion-nucleon amplitudes. In result, this approach correctly reproduce pions -- nucleon amplitudes(with the Born -- diagrams contributions, too).