On the effective quark potential in baryons

The splitting of the non-strange members of the first excited level [70,1-]1 of baryon resonances is analysed. The spin-dependent forces (spin-spin, spin-orbit, tensor) are supposed to arise from the Coulomb term due to one-gluon exchange, from the long-range linearly rising part of the potential, and from additional 'hard-core' spin-spin terms which may be generated by higher-order graphs contributing to the qq kernel. For the long range part it is assumed either that it comes from a superposition of a vector and a scalar kernel of the form epsilon(γsup(μ) X γsub(μ) X 1) + (1 - epsilon)(1 X 1 X 1) (+ permutations), or, alternatively, that it arises from a vector exchange with an anomalous moment kappa in the quark-gluon vertex. Values of epsilon approximately 0 or kappa approximately -1 turn out to be favoured. The strong coupling constant and the slope of the linear potential come out in the correct order of magnitude. Very large hard-core spin-spin terms are needed. This fact makes the determination of the effective potential from the underlying theory of quantum chromodynamics as well as the phenomenological analysis of the observed spectra rather problematic. (Auth.)