${\Theta }^{+}$-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.

Comments: 5 pages, 1 figure