Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the thoery contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second derivative term perturbatively and show that the SFN model with the second derivative term possesses soliton solutions.