document: The spins and parities of Θ+ and Ξ−− are not yet known experimentally. In this new wave of pentaquark research, most theoretical papers take the spin equal to 1/2. The parity is more controversial. In chiral soliton or Skyrme models the parity is positive [4]. In constituent quark models it is usually positive. In the present approach, the parity of the pentaquark is given by P=(−)ℓ+1, where ℓ is the angular momentum associated with the relative coordinates of the q4 subsystem. We analyze the case where the subsystem of four light quarks is in a state of orbital symmetry [31]O and carries an angular momentum ℓ=1. Although the kinetic energy of such a state is higher than that of the totally symmetric [4]O state, the [31]O symmetry is the most favourable both for the flavour–spin interaction [12] and the colour–spin interaction [13]. In the first case the statement is confirmed by the comparison between the realistic calculations for positive parity [12] and negative parity [14], based on the same quark model [15]. In Ref. [12] the antiquark was heavy, c or b, and accordingly the interaction between light quarks and the heavy antiquark was neglected, consistent with the heavy quark limit. In Ref. [16] an attractive spin–spin interaction between s̄ and the light quarks was incorporated and shown that a stable or narrow positive parity uudds̄ pentaquark can be accommodated within such a model. This interaction has a form that corresponds to η meson exchange [17] and its role is to lower the energy of the whole system.
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