$Θ^+$-pentaquark parity from associative baryon production in $πD$ collisions, $π^{\pm}+D\to Θ^+ +Σ^{\pm}$

Abstract

We derive, in model independent way, the spin structure of the matrix element for the reaction of associative $Θ^+$ pentaquark production, $π^{\pm}+D\to Θ^+ +Σ^{\pm}, $ 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 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 $Σ^{\pm}$ polarization on the vector and tensor deuteron polarizations, are insensitive to the $Θ^+$ parity in the considered kinematical conditions. All linear and quadratic relations between polarization observables in $π^{\pm}+\vec D\to Θ^+ +\vecΣ^{\pm}(Θ^+ $ is unpolarized) do not depend on the parity of the $Θ^+$ pentaquark.