Near-BPS Skyrmions

We consider the Skyrme model in the near-BPS limit. The BPS part is made of the sextic term plus a potential and the deformation is made of the standard massive Skyrme model controlled by a small parameter epsilon << 1. In order to keep the perturbation under theoretical and computational control, we find a model for which BPS Skyrmions have compact support, henceforth denoted as compactons, and the spherically symmetric B = 1 Skyrmion represents the most stable solution. We use the epsilon-expansion scheme to systematically calculate the corrections to the energy and compare with the exact numerical computations in the B = 1 sector. Finally, we use the epsilon-expansion scheme to calculate the bound state of two B = 1 Skyrmions and its binding energy, which corresponds, prior to quantization, to the deuteron in our model.