$\Theta^+$-pentaquark parity from associative baryon production in $\pi D$ collisions, $\pi^{\pm}+D\to \Theta^+ +\Sigma^{\pm}$

Abstract

We derive, in model independent way, the spin structure of the matrix element for the reaction of associative $\Theta^+$ pentaquark production, $\pi^{\pm}+D\to \Theta^+ +\Sigma^{\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 $\Theta^+ .$ We have proved that such reaction can be used for a model independent determination of the P-parity of $\Theta^+$ only by measuring the $\Theta^+$ polarization. Other polarization observables, such as the dependence of the $\Sigma^{\pm}$ polarization on the vector and tensor deuteron polarizations, are insensitive to the $\Theta^+$ parity in the considered kinematical conditions. All linear and quadratic relations between polarization observables in $\pi^{\pm}+\vec D\to \Theta^+ +\vec\Sigma^{\pm}(\Theta^+ $ is unpolarized) do not depend on the parity of the $\Theta^+$ pentaquark.