Spinning skyrmions and the Skyrme parameters

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 Letter 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 cannot 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.