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(cqs)>~M(cqq)+M(css).