Model dependence in the photoproduction of kaons from protons and deuterons

Abstract

The reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ and $\ensuremath{\gamma}d\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}n$ have been investigated over the energy range from ${E}_{\ensuremath{\gamma}}=1.0\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}{E}_{\ensuremath{\gamma}}=1.8\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ in a tree-level effective Lagrangian model that incorporates most of the well-established resonances of spins $\frac{1}{2}$ and $\frac{3}{2}$ below $1.9\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$. Several sets of values for the resonance couplings are generated by fitting empirical cross section curves for the proton reaction at three different energies. Results obtained with a number of these fits are then presented for the cross sections and several single polarization observables for both reactions. The deuteron reaction is treated within the impulse approximation with final state interactions incorporated by means of a nonrelativistic overlap integral in momentum space. We explore the dependences of the calculated quantities on several facets of the model, including the particular resonance fit employed, the treatment of the spin $\frac{3}{2}$ resonance propagator, the prescription used for the resonance widths, and for the deuteron reaction, the final state interaction and deuteron wave function employed. We find that for neither reaction are the cross sections very sensitive to any of the model details. The polarization observables, on the other hand, are quite sensitive to certain model details, particularly to the resonance model employed and to the prescription used for the resonance widths. In general the polarization observables in the proton reaction are more sensitive to model details than the polarization observables in the deuteron reaction. The calculated deuteron observables are not strongly dependent on either the final state interaction or the deuteron wave function employed.