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

The cross section for ${ϴ}^{+}$ production from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$, which was observed in the CLAS experiment at the Jefferson National Laboratory, is evaluated in a hadronic model that includes couplings of ${ϴ}^{+}$ to both $KN$ and $K^{*}N$. With their coupling constants determined from the empirical $\pi NN\left(1710\right)$ and $\rho NN\left(1710\right)$ coupling constants using the SU(3) symmetry, the cross section for this reaction has been evaluated by taking ${ϴ}^{+}$ to have spin 1∕2 and isospin 0 but either positive or negative parity. We find that if ${ϴ}^{+}$ has positive parity as predicted by the chiral soliton model and the correlated quark model, the cross section is $50–110\text{nb}$, depending on the value of the $K^{*}Nϴ$ coupling. The cross section is reduced by more than a factor of 10 if ${ϴ}^{+}$ has negative parity as given by lattice QCD studies and the uncorrelated quark model. For both parities, the differential cross section peaks at small negative four-momentum transfer when the reaction is dominated by the $t$-channel kaon-exchange diagram that involves only the coupling of ${ϴ}^{+}$ to $KN$. After decreasing with increasing negative four-momentum transfer, the differential cross section increases again when the $u$-channel contribution due to intermediate ${ϴ}^{+}$ propagation becomes important at large negative four-momentum transfer.

Figure 1

Diagrams for ${ϴ}^{+}$ production from the reaction $\gamma p\to {\overline{K}}^{*0}{ϴ}^{+}$.

Figure 2

Total cross section for the production of positive parity ${ϴ}^{+}$ from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$ as a function of photon energy obtained without form factors and for the coupling constant $g_{K^{*}Nϴ}=1.8$ (dotted curve), 0 (solid curve), and $-1.8$ (dashed curve).

Figure 3

(Color online) Same as Fig. 2 with form factors.

Figure 4

(Color online) Differential cross section for production of a positive parity ${ϴ}^{+}$ from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$ at $E_{\gamma }=3$, 4, 5, and $6\text{GeV}$ obtained with form factors and for the coupling constant $g_{K^{*}Nϴ}=1.8$ (dotted curves), 0 (solid curves), and $-1.8$ (dashed curves).

Figure 5

(Color online) Total cross section for the production of negative parity ${ϴ}^{+}$ from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$ as a function of photon energy for the coupling constant $g_{K^{*}Nϴ}=0.25$ (dotted curve), 0 (solid curve), and $-0.25$ (dashed curve).

Figure 6

(Color online) Differential cross section for production of a negative parity ${ϴ}^{+}$ from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$ at $E_{\gamma }=3$, 4, 5, and $6\text{GeV}$ obtained with form factors and for the coupling constant $g_{K^{*}Nϴ}=0.25$ (dotted curves), 0 (solid curves), and $-0.25$ (dashed curves).

Figure 7

Diagram for ${ϴ}^{+}$ production from the reaction $\gamma p\to {\pi }^{+}{K}^{-}{ϴ}^{+}$ via $K^{*-}$ exchange.