Spin dependence of the masses of heavy baryons.

Recently, Falk [1] has proposed that there exist two undiscovered heavy baryons: a Σc(2380) that decays radiatively to the Λc, and a Σb(5760) that decays radiatively to the Λb. In this note I use the systematics of the spin-dependent forces between quarks to argue against the existence of these two new states. The same ideas suggest that two of the proposed “equal spacing rules” [1] among heavy baryon mass differences should be replaced by inequalities. Tensor and spin-orbit forces do not contribute perturbatively to the masses of ground-state baryons and so I confine myself to baryons without radial or orbital excitations. Then only the spin-spin interaction (sometimes called the color-magnetic or color-hyperfine interaction) survives in the perturbative approximation. More detailed discussions of these points have been given previously [2,3]. In addition to treating baryon mass splittings, I also consider the spin-dependent splittings of meson masses, as under certain assumptions there are inequalities relating meson and baryon mass differences. I neglect mass splittings among isospin multiplets, which means neglecting electromagnetic effects and the mass difference between the d and u quark Also, as is often done, I let the symbol for a hadron denote its mass, averaged over isospin states if more than one exists. In order to motivate certain inequalities among matrix elements of the spinspin interaction, it is convenient to assume [2,3] that the form of the spin-spin interaction IS between quarks in a baryon or a quark and an antiquark in a meson has the form IS = −3 ∑