Why the Σ and Ξ hyperfine splittings are different

Abstract

The Σ and Ξ splittings, predicted to be equal in the SU(6) quark model, are shown to differ because the smaller size of the Ξ wave function enhances the short-range hyperfine interaction. The change in the relative motion of a u-s pair in the hyperon produced by a change in the mass of the third quark is not a simple scale change and is sensitive to details of the interquark potential. This effect is absent in the harmonic oscillator model, where the third quark is completely decoupled from the relative motion within the other pair, but is appreciable and has the right order of magnitude in the logarithmic potential model.