Θ⁺-Pentaquark parity from associative baryon production in πd collisions, π ^± + d → Θ⁺ + Σ^±

Abstract

We derive, in model-independent way, the spin structure of the matrix element for the reaction of associative Θ⁺-pentaquark production, π ^± + d → Θ⁺ + Σ^±, in the threshold region and in collinear kinematics. The expressions for the polarization observables in this reaction are found assuming spin 1/2 and different parities for Θ⁺. We have proved that such a reaction can be used for a model-independent determination of the P parity of Θ⁺ only by measuring the Θ⁺ polarization. Other polarization observables, such as the dependence of the Σ^± polarization on the vector and tensor deuteron polarizations, are insensitive to the Θ⁺ parity under the considered kinematical conditions. The linear and quadratic relations between polarization observables in $\pi ^ \pm + \vec d \to \Theta ^ + + \vec \sum ^ \pm$ (Θ⁺ is unpolarized) do not depend on the parity of the Θ⁺ pentaquark. The analysis performed for this reaction is also applicable without any modification to the reaction K ⁺ + d → Θ⁺ + p. Using the pole model for the reaction mechanism, we estimated the value of the cross section for the reaction K ⁺ + d → Θ⁺ + p near the threshold.