Pion Fluctuations about the Skyrmion

Abstract

Recently, there is an increasing interest in the Skyrme modeP) as an effective field theory of baryons underlied by the QeD. By means of a collective coordinate method) static properties of nucleons have been shown to be reproduced well in the model. Another interesting feature of the model is to predict an inner repulsion of about 1 Ge V in the overlapping two nucleons, in addition to a prediction of asymptotic one-pion exchange interaction at longer distances.) The model now enjoys several applications and extentions. Fluctuations about a classical soliton solution in the Skyrme model (Skyrmion) are considered to describe excitation modes of baryons and mesonic interactions. Several authors have attempted to calculate breathing modes of nucleons:)-8) An interesting point is that the excitation energies are suggested to be considerably small compared with experiment, while a simple quark model predicts too high excitations. Such investigations have been recently extended to general partial waves of the fluctuation modes, and interesting features of the Skyrme model have been derived.7).B) In Ref. 7), the authors noted that coupling terms involving spin and isospin are lacked in the method, and that a quantum number A = I + I is obtained as a conserved quantity, where I is the orbital angular momentum and I the isospin of the pion field. They afterwards proposed a recoupling scheme to connect the former result with that of physical channels.8) In this paper we want to show that a chiral perturbation method of Schnitzer) for the fluctuating field resolves this problem naturally. The Skyrme model assumes the lagrangian of the field as + l2 e-zTr{[(oU) U t , (ovU)U t ),}