Surviving and Spurious Yukawa Couplings in the Skyrmion Model

Abstract

1. It has been pointed out/H) within the present quantization algorithm of the Skyrmion model, that a pion-Skyrmion Yukawa coupling term vanishes from the pion-Skyrmion effective Lagrangian, where an asymptotically free pion field is introduced as quantum fluctuation about a classical Skyimion configuration. It was Skyrme himself who first pointed out this.4) If we have no ~oupling terms linear in the pion field at all, the iI state ~annot decay into N7r, and P-wave pion-nucleon scattering amplitudes do not develop nucleon poles. In order to construct a state with definite spin and isospin values such as Nand ii, we have to rotate the Skyrmion and project it on a definite spin and isospin state. The rotated Skyrmion described in terms of collective coordinates is not an exact solution of the equations of motion. Due to this breaking of the equations of motion at order Nc - a term linear in the pion field survives at order Nc -3/2. The surviving linear term has been regarded as the missing Yukawa coupling which gives rise to the iI decay,5)-8) while the present author9) has claimed that it is hard to regard such a surviving Yukawa coupling as the proper Yukawa couplings which are determined by experiments. On the other hand, there is an argumeneO),ll) that the Yukawa couplings of order INc exist also in a soliton model, but due to the cancellation between the leading terms the resultant Born terms become order 1. If this is the case, the defect of the vanishing Yukawa coupling is an illusion: But, the Born terms appear only as a result of the inadequate application of the reduction formula) to meson-soliton scattering amplitudes. In this paper we give additional arguments against the validity of the surviving Yukawa coupling and also of the spurious Born terms.