The pentaquark spectrum from Fermi statistics

Abstract

AbstractWe 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)$$_f$$ f , two with spin 1/2 and one with spin 3/2, in line with the observed, strangeness $$S=0,-1$$ S = 0 , - 1 , spectrum. Additional lines corresponding to decays into $$J/\psi +\Sigma $$ J / ψ + Σ and $$J/\psi +\Xi $$ J / ψ + Ξ are predicted. In the language of non-relativistic SU(6), ground state pentaquarks form either a $${\varvec{56}}$$ 56 or a $${\varvec{20}}$$ 20 representation, distinguished by presence or absence of pentaquarks decaying in the spin 3/2 decuplet, e.g. in $$J/\psi +\Delta ^{++}$$ J / ψ + Δ + + . Observation of a strangeness $$S=-2$$ S = - 2 or isospin $$I=3/2$$ I = 3 / 2 pentaquarks would be a clear signature of compact, QCD bound pentaquarks.