Deformation of the CP(1) model leading to fixed size solitons in 2+1 dimensions

We discuss static particle-like solitons in the 2+1 dimensional CP(1) model with a small mass deformation $m$ preserving a $U(1)\times Z_2$ symmetry in the Lagrangian. Due to the breaking of scale invariance, the energy function becomes a strictly increasing function of the soliton size $\rho$, and therefore no classical finite size solution exists in this model. To remedy this we employ a well known technique of introducing a forth-order derivative term in the Lagrangian to force the soliton action to diverge at small values of $\rho$. With this additional term the action exhibits a stable minimum at fixed size $\rho$.