Pentaquark Symmetries, Selection Rules and another potentially Narrow State

F. E. Close, J. J. Dudek

Published 2004-01-24, updated 2004-01-30Version 2

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 $\Xi_5 \to \Xi^*\pi$ 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 $g^2(\Theta_Q N K_Q^*)/g^2(\Theta_Q N K_Q) = 3$ 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.