A Mass Inequality for the ${\Xi }^{\ast }$ and ${\Theta }^{+}$ Pentaquarks

Abstract

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

Comments: revtex, 5 pages, no figures; added discussion of spin-orbit effects and recent experimental references