Skyrmion-anti-Skyrmion annihilation with ω mesons

We study numerically the annihilation of an ω-stabilized Skyrmion and an anti-Skyrmion in three spatial dimensions. To our knowledge this is the first successful simulation of Skyrmion-anti-Skyrmion annihilation which follows through to the point where the energy is carried by outgoing meson waves. We encounter instabilities similar to those encountered is earlier calculations, but in our case these are not fatal and we are able to simulate through this process with a global energy loss of less than 8% and to identify robust features of the final radiation pattern. The system passes through a singular configuration at the time of half-annihilation. This is followed by the onset of fast oscillations which are superimposed on the smoother process which leads to the appearance of outgoing waves peaked at roughly 45° to the incident direction. We investigate the two prominent features of this process: the proliferation of small, fast oscillations and the singular intermediate configuration. We find that our equations of motion allow for a regime in which the amplitude of certain small perturbations increases exponentially. This regime is similar but not identical to the situation pointed out earlier regarding the original Skyrme model. We argue that the singularity may be seen as the result of a pinch effect similar to that encountered in plasmas.