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