Photoproduction of the ${\Theta }^{+}$ pentaquark in Feynman and Regge theories

Photoproduction of the ${\Theta }^{+}$ pentaquark on the proton is analyzed by using isobar and Regge models. The difference in the calculated total cross section is found to be more than two orders of magnitude for a hadronic form-factor cutoff $\Lambda >1\mathrm{GeV}$. Comparable results would be obtained for $0.6\le \Lambda \le 0.8\mathrm{GeV}$. The contribution of the ${\Theta }^{+}$ photoproduction to the GDH integral is also calculated. By comparing with the current phenomenological calculation, it is found that the GDH sum rule favors the result obtained from the Regge approach and isobar model with small Λ.

Figure 1

Feynman diagrams for ${\Theta }^{+}$ photoproduction on the proton: $\gamma +p\to {\overline{K}}^0+{\Theta }^{+}$.

Figure 2

Total cross sections ${\sigma }_T$ and $-{\sigma }_{{\mathrm{TT}}^{\text{'}}}$ of the isobar and Regge models. In the isobar model, variation of the total cross section for different hadronic form-factor cutoffs is shown.

Figure 3

Contribution of the ${\Theta }^{+}$ photoproduction to the GDH integral of the proton for isobar (with different hadronic form-factor cutoffs) and Regge models.

Figure 4

Differential cross section for ${\Theta }^{+}$ photoproduction on the proton as functions of $\cos \theta$ and W from the isobar model obtained with $\Lambda =1\mathrm{GeV}$. The same pattern, but with a magnitude 20 times smaller, would be obtained if one used $\Lambda =0.6\mathrm{GeV}$.

Figure 5

Differential cross section for ${\Theta }^{+}$ photoproduction on the proton as functions of $\cos \theta$ and W from the Regge model.