Model-independent methods to measure the $P$-parity of the $\Theta^+$-pentaquark in photoproduction experiments

Abstract

We discuss model independent methods to measure the $P$-parity of the $\Theta^+$-pentaquark, in the simplest processes of photoproduction, $\gamma+N\to \bar{K}+\Theta^+$, using definite relations between T-even polarization observables, which depend on the $P$-parity of the $\Theta^+$ baryon (with respect to the $NK$ system). One method, which holds for any photon energy and any $K$ meson production angle, is based on the relation between the $\Sigma_B$ asymmetry (induced by a linearly polarized photon beam, with unpolarized target) and the $D_{nn}$ component of the depolarization tensor (for unpolarized photon beam). Another method, which applies in collinear kinematics (or in threshold conditions), is related to the sign of the $D_{nn}$ component, with linearly polarized photon beam.