Baryon Mass Inequalities in Quark Models

Recently conjectured three- (and more-) body mass inequalities are investigated for the quark models of baryons in which it is assumed that baryon masses are the ground-state energies of Schrödinger-type operators with pair potentials $V$. It is proved that these inequalities hold (even with a "relativistic" form for the kinetic energy) if $V$ belongs to a certain class (which includes many potentials commonly used), but that they do not hold for all $V$ (even in the nonrelativistic case). One example of our results is $2M\left(\mathrm{cqs}\right)\mathrm{}>~M\left(\mathrm{cqq}\right)+M\left(\mathrm{css}\right)\mathrm{}$.