A Mass Inequality for the $Ξ^*$ and $Θ^+$ Pentaquarks
We derive an upper bound on the mass difference between the $Ξ^*$ and $Θ^+$ pentaquarks which are the manifestly exotic members of the $SU(3)_f$ antidecuplet. The derivation is based on simple assumptions about $SU(3)_f$ symmetry breaking and uses the standard quantum mechanical variational method. The resulting rather robust bound is more than 20 MeV below the experimentally reported $Ξ^*-Θ^+$ mass difference, emphasizing the need for confirmation of the experimental mass values and placing strong constraints on quark models of the pentaquark structure.