Decay Probability Ratio of Pentaquark Theta^+ State

Abstract

The pentaquark state of ${\Theta }^{+}(uudd\bar{s})$ has been observed to decay with two decay modes: ${\Theta }^{+}\to n{K}^{+}$ and ${\Theta }^{+}\to p{K}^0$. The decay probability ratio of the two decay modes is studied with general symmetry consideration of isospin, spin, and parity. We arrive at a result of the ratio $\frac{\Gamma ({\Theta }^{+}\to n{K}^{+})}{\Gamma ({\Theta }^{+}\to p{K}^0)}=\frac{(\alpha -\beta {)}^2}{(\alpha +\beta {)}^2}(\frac{k_1}{k_2}{)}^{2L+1}$, which is valid for the ${\Theta }^{+}$ state to be a pure isoscalar or isovector state, or an isoscalar and isovector mixing state, or an isotensor state with mixture of isoscalar and isovector components with coefficients $\alpha$ and $\beta$. The dependence on spin and parity of the pentaquark ${\Theta }^{+}$ state is found to be small due to small difference between the center of mass decay momenta $k_1$ and $k_2$ of the two decay modes. We also provide an analysis on the constraint of the isospin of ${\Theta }^{+}$ from the absence of a peak in the $p{K}^{+}$ invariant mass distribution in the $\gamma p\to p{K}^{+}{K}^{-}$ process. Future experimental results about the decay probability ratio may provide information about the properties of the pentaquark ${\Theta }^{+}$ state.

Comments: 8 latex pages, version for publication, a typo corrected