Pentaquark States and Spectrum

We present a general classification scheme for qqqqbar q pentaquark states in terms of spin-flavour SU(6) representations and their decomposition in terms of SU_f (3) ⊗ SU_s (2). Special attention is paid to the S₄ permutational symmetry of the spin-flavour part of the four-quark wave functions. This classification is general and useful both for experimentalists and model builders. In particular, it will be useful also for the construction of higher three-quark Fock components or to compare with the nonrelativistic limits of other models. We discuss the spectroscopy of pentaquarks using a Gürsey-Radicati type mass formula, whose coefficients have been determined previously in a study of qqq baryons. Its angular momentum depends on the interplay between the spin-flavour and orbital contributions to the mass operator. The magnetic moment of the Θ⁺(1540) is discussed in the constituent quark model for different values of angular momentum and parity. Finally we construct a model for the five-body problem that can be solved exactly: the properties of the pentaquark are discussed in a collective string-like model.