Effective Lagrangian for Skyrmion physics

The effective chiral Lagrangian for low-energy pion-Skyrmion physics is considered as an expansion in powers of (partialPhi), where Phi is the chiral field. The O((partialPhi)/sup 2/) term is the nonlinear sigma-model Lagrangian L/sub 2/. Two theoretical approaches to the higher-order terms are examined. The first involves integration over fermion degrees of freedom. The O((partialPhi)/sup 4/) terms obtained this way, together with L/sub 2/, are found to be consistent with low-energy ..pi pi.. phase shifts: in particular, in the dominant rho and sigma channels. In the second approach, an effective pion Lagrangian is generated by integrating some simple chiral meson-field Lagrangians over the heavy mesons. At O((partialPhi)/sup 4/) two terms are found: a term L/sub 4,rho/ of Skyrme form, with a model-independent coefficient determined by the rho mass, and a non-Skyrme term L/sub 4,sigma/, the coefficient of which is more model dependent and determined by the sigma mass; both terms are compatible with the fermion integration results. It is concluded that the O((partial..pi..)/sup 4/) terms are well established theoretically, and in good qualitative agreement with pion data. These terms do not, however, stabilize the soliton. Some discussion of the possible stabilizing effects of O((partial..pi..)/sup 6/) terms is given.