The pentaquark spectrum from Fermi statistics

Abstract

We study compact hidden charm pentaquarks in the Born–Oppenheimer approximation, previously introduced for tetraquarks, assuming the heavy pair to be in a color octet. We show that Fermi statistics applied to the complex of the three light quarks, also in color octet, requires S-wave pentaquark ground states to consist of three octets of flavour-SU(3)_f, two with spin 1/2 and one with spin 3/2, in line with the observed, strangeness S=0,-1, spectrum. Additional lines corresponding to decays into J/psi +Sigma and J/psi +Xi are predicted. In the language of non-relativistic SU(6), ground state pentaquarks form either a {varvec{56}} or a {varvec{20}} representation, distinguished by presence or absence of pentaquarks decaying in the spin 3/2 decuplet, e.g. in J/psi +Delta ^{++}. Observation of a strangeness S=-2 or isospin I=3/2 pentaquarks would be a clear signature of compact, QCD bound pentaquarks.