Pentaquark ${\Theta }^{+}$ production from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{\Theta }^{+}$

Abstract

The cross section for ${\Theta }^{+}$ production from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{\Theta }^{+}$, which was observed in the CLAS experiment at the Jefferson National Laboratory, is evaluated in a hadronic model that includes couplings of ${\Theta }^{+}$ to both $KN$ and $K^{\ast }N$. With their coupling constants determined from the empirical $\pi NN(1710)$ and $\rho NN(1710)$ coupling constants using the SU(3) symmetry, the cross section for this reaction has been evaluated by taking ${\Theta }^{+}$ to have spin 1/2 and isospin 0 but either positive or negative parity. We find that the cross section is 10-15 nb if ${\Theta }^{+}$ has positive parity as predicted by the chiral soliton model. The cross section is reduced by more than a factor of 10 if ${\Theta }^{+}$ has negative parity as given by lattice QCD studies. For both parities, the differential distribution peaks at small negative four momentum transfer as expected from the dominating $t$-channel kaon-exchange diagram that involves only the coupling of ${\Theta }^{+}$ to $KN$.

Comments: 15 pages, 7 figures