document: In the bag model and in linear or harmonic oscillator confining potentials, the first excited S-state lies above the lowest P-state, making the predicted Roper mass heavier than the lightest negative parity baryon mass. Pairwise spin-dependent interactions must reverse the level ordering. As mentioned earlier, color-spin interactions fail in this regard [29], while flavor-spin interactions produce the desired effect. Since the q3 color wave function is antisymmetric, the flavor-spin-orbital wave function is totally symmetric. For all quarks in an S-state, the flavor-spin wave function is totally symmetric all by itself and leads to the most attractive flavor-spin interaction. If one quark is in a P-state, the orbital wave function is mixed symmetry and so is the flavor-spin wave function, and the flavor-spin interaction is a less attractive. In the SU(3)F symmetric case, Eq. (1), one obtains mass splittings (2)ΔMχ=−14Cχ,N(939),N∗(1440),−4Cχ,Δ(1232),−2Cχ,N∗(1535). Here we have approximated the N∗(1535) as a state with total quark spin-1/2.
extractive_keyphrases: bag model level ordering mass splittings orbital wave function oscillator confining potentials q3 color wave function quark quarks
abstractive_keyphrases: color-spin interactions flavor-spin interaction flavor-spin interactions flavor-spin-orbital wave function flavor-spin wave function pairwise spin-dependent interactions quark spin