Pentaquark Decay Amplitudes From SU(3) Flavor Symmetry

The experimental signature of an S=+1 baryon of mass 1540 MeV and width 10-25 MeV has led to speculation that this is an exotic baryon consisting of 4 quarks and 1 antiquark lying at the top of a $\bar{10}$ SU(3) multiplet. The observed decay modes are $\Theta^{+} \to K^{+}n$ and $\Theta^{+} \to K^0_Sp$ or in terms of flavor multiplets, $\bar{10}$ to 8 x 8. The effective Hamiltonian for this decay can be written as a flavor singlet piece plus an SU(3) breaking term. By using the Wigner-Eckart thereom, we then relate the decay amplitudes of all 10 members of the antidecuplet in terms of 5 parameters. Similarly, we perform the same calculation for the proposed exotic multiplets 27 and 35.