Pentaquark Symmetries, Selection Rules and another potentially Narrow State

Abstract

We identify essential differences between the pentaquark and chiral soliton models of \10bar${}_5$ and {\bf 8}${}_5$ pentaquarks and conventional {\bf 8}${}_3$ states, which are experimentally measurable. We show how the decays of ${\Xi }_5$ states in particular can test models of the pentaquarks, recommend study of the relative branching ratios of e.g. ${\Xi }_5^{-}\to {\Xi }^{-}{\pi }^0:{\Xi }^0{\pi }^{-}$, and predict that the decay amplitude ${\Xi }_5\to {\Xi }^{\ast }\pi$ is zero at leading order in pentaquark models for any mixture of \10bar and the associated {\bf 8}${}_5$. We also include a pedagogic discussion of wavefunctions in the pentaquark picture and show that pentaquark models have this {\bf 8}${}_5$ with $F/D=1/3$, in leading order forbidding ${\Xi }_5\to \Lambda K$. The role of Fermi-Dirac symmetry in the $qqqq$ wavefunction and its implications for the width of pentaquarks are briefly discussed. The relative couplings $g^2({\Theta }_{Q}N{K}_Q^{\ast })/g^2({\Theta }_{Q}N{K}_Q)=3$ for $Q\equiv s,c,b$. A further potentially narrow state $\Lambda$ in {\bf 8}${}_5$ with $J^P=3/2^{+}$ is predicted around 1650 MeV.

Revised version, corrects PDF margin problems, minor changes to text

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