A Mass Inequality for the $\Xi^*$ and $\Theta^+$ Pentaquarks

Abstract

We derive an upper bound on the mass difference between the $\Xi^*$ and $\Theta^+$ 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 $\Xi^*-\Theta^+$ mass difference, emphasizing the need for confirmation of the experimental mass values and placing strong constraints on quark models of the pentaquark structure.