Phenomenological Analysis ofK+ΛPhotoproduction

Low-energy $K\Lambda$ photoproduction cross-section and polarization data are analyzed using contributions from nonresonant perturbation amplitudes associated with $p$, $K^{+}$, $\Lambda$, $\Sigma$, and $K^{*+}$ propagators, and from a resonant amplitude in one total and final orbital angular momentum state. The resonance is assumed to have an energy of about 1.7 GeV and a width of about 100 MeV. The data are analyzed by assuming that the resonance can be in any one of the angular momentum states from $S_{\frac{1}{2}}$ to $F_{\frac{5}{2}}$, and a ${\chi }^2$ minimization is performed for each possibility. It is found that the perturbation amplitudes alone give good fits to the cross-section data, and that only a small amount of resonant amplitude in any one of a number of angular momentum states is sufficient to explain the polarization without strongly modifying the cross-section fits. The assumed resonant state in general contributes about 20% to the total cross section, and $P_{\frac{1}{2}}$ and $D_{\frac{3}{2}}$ states give the lowest values of ${\chi }^2$. The values of the coupling constants obtained herein are compared with those expected from $\mathrm{SU}\left(3\right)\mathrm{}$; approximate agreement is found though the values obtained in our analysis are generally smaller than the $\mathrm{SU}\left(3\right)\mathrm{}$ predictions. The possible contribution of an $F_{\frac{5}{2}}$ resonant amplitude found in the analysis is consistent with that expected from $\mathrm{SU}\left(3\right)\mathrm{}$ for the third resonance. A compilation of all the presently existing $K\Lambda$ photoproduction data is given as an appendix.