The quantization of the B=1 and B=2 Skyrmions

TL;DR

This paper investigates the quantization of B=1 and B=2 Skyrmions, focusing on parameter fitting and deformation effects, revealing challenges in simultaneously fitting nucleon and deuteron masses with standard parameters.

Contribution

It introduces a method to optimize Skyrme parameters using axial deformations and simulated annealing, highlighting limitations in current models for reproducing both nucleon and deuteron masses.

Findings

Axial deformations significantly reduce rotational energy.

A common parameter set cannot fit both nucleon and deuteron masses for standard pion masses.

Additional terms or higher pion masses may be necessary for accurate modeling.

Abstract

We propose to set the Skyrme parameters F_{\pi} and e such that they reproduce the physical masses of the nucleon and the deuteron. We allow deformation using an axially symmetric solution and simulated annealing to minimize the total energy for the B=1 nucleon and B=$ deuteron. First we find that axial deformations are responsible for a significant reduction (factor of \approx 4) of the rotational energy but also that it is not possible to get a common set of parameters F_{\pi} and e which would fit both nucleon and deuteron masses simultaneously at least for m_{\pi}= 138 MeV, 345 MeV and 500 MeV. This suggests that either m_{\pi}>500 MeV or additional terms must be added to the Skyrme Lagrangian.