Spinning Skyrmions and the Skyrme Parameters

TL;DR

This paper investigates the impact of removing the rigid body approximation in the Skyrme model, revealing that realistic pion mass values prevent reproducing nucleon and delta masses, which influences multi-Skyrmion structures.

Contribution

It introduces numerical calculations that allow Skyrmion deformation, challenging the standard rigid body approximation and showing the importance of pion mass in parameter fitting.

Findings

Rigid body approximation leads to artifacts in Skyrme parameters.

Realistic pion mass prevents reproducing nucleon and delta masses.

Larger pion mass values enable mass reproduction, affecting multi-Skyrmion structures.

Abstract

The traditional approach to fixing the parameters of the Skyrme model requires the energy of a spinning Skyrmion to reproduce the nucleon and delta masses. The standard Skyrme parameters, which are used almost exclusively, fix the pion mass to its experimental value and fit the two remaining Skyrme parameters by approximating the spinning Skyrmion as a rigid body. In this paper we remove the rigid body approximation and perform numerical calculations which allow the spinning Skyrmion to deform and break spherical symmetry. The results show that if the pion mass is set to its experimental value then the nucleon and delta masses can not be reproduced for any values of the Skyrme parameters; the commonly used Skyrme parameters are simply an artifact of the rigid body approximation. However, if the pion mass is taken to be substantially larger than its experimental value then the nucleon and delta masses can be reproduced. This result has a significant effect on the structure of multi-Skyrmions.