Hadron dynamics in the 3-flavor Skyrme model

We present the S-flavor formalism for scattering pseudoscalar mesons from baryons in the class of models in which the baryon is viewed as a “hedgehog” soliton in the meson field. To test this formalism, we apply it to ~FN scattering in the Skyrme model. The result, as compared with the 2-flavor Skyrme model, is an overall improvement in agreement with experiment. Submitted to Physical Review Letters * Work supported by the Department of Energy, contract D E A C 0 3 7 6 SF 00 5 15. Despite universal acceptance of the quark model, recent times have seen a revival of interest in Skyrme’s imaginative treatment of the baryon as a soliton in the field of pions.’ The soliton picture of the baryon can be motivated from a consideration of QCD in the limit in which N,, the number of colors, is taken to infinity. 2’3 The popularity of the Skyrme model in particular is largely due to the ease with which it permits moderately accurate calculations of a wide variety of hadronic properties. 4’5 The starting point is the modified nonlinear a-model: L = g Trd,Ud’Ut + 16 & Tr[(d,U)Ut, (bU)Ut]2, u E SU(2), (1) which admits a hedgehog soliton solution (“skyrmion”) UO = exp{iF(r)P -3) , (2) where F solves a nonlinear variational equation. Of course, any rotation AUoA-1 is an equally acceptable solution; indeed, the proper identification of (2) with a nucleon or A requires the quantization of the “collective coordinates” A.4 Pions can readily be added to the modellg by considering fluctuations about the skyrmion: 2o UO + exp{F(r)i: + 277(x, t)/fT}. (3) In so doing one can explicitly calculate the S-matrix for zN scattering and in the process obtain the spectrum of N and A resonances, with surprisingly good results: rough qualitative agreement for most partial-wave amplitudes, ‘JO and 8% agreement on average with experimental resonance masses.” In addition, using only the hedgehog structure of the skyrmion, one can derive model-independent