Use of theρ-Photon Analogy in a Model of Isobar Production

A model for the production of isobars by the exchange of a spin-1 meson is presented. In particular we discuss the production of the $N^{*}\mathrm{}\left(1238\right)\mathrm{}$ and $Y^{*}\mathrm{}\left(1380\right)\mathrm{}$ $P_{\frac{3}{2}}$ isobars by $\pi$, $K^{+}$ and $K^{-}$ mesons by the exchange of $\rho$ or $K^{*}$. The vertex $\rho +N\to N+\pi$ or ${\overline{K}}^{*}+N\to \Lambda +\pi$ is treated by assuming a magnetic dipole transition ($M1\mathrm{}\to P_{\frac{3}{2}}$) in analogy with virtual photoproduction (electroproduction). This assumption then leads to a prediction for the decay distribution, the over-all production distribution and the mass distribution of the isobar with no free parameters. This description is found to be in agreement with experiment in a variety of cases, although to obtain quantitative agreement with the production angular distributions at higher energies a form factor must be assumed to give sufficient backward peaking for the isobar. It is further shown how the absolute cross section for isobar production by this mechanism may be found in terms of the photo-production cross section by assuming the "$\rho$-photon analogy" (i.e., total $\rho$ dominance of isovector photon interactions) which at zero momentum transfer reads $\left(\frac{1}{e}\right)〈{J_{\mu }}^{\gamma v}〉=\left(\frac{1}{f_{\rho }}\right)〈{J_{\mu }}^{\rho }〉.$ The resulting number is reasonable as far as order of magnitude is concerned. To make a quantitative comparison with experimental cross sections, the reaction $K^{+}+P\to N^{*++}+K^0$, where some detailed information exists, is examined. The value of the $\rho \mathrm{KK}$ coupling needed here is found in terms of the known $\rho \pi \pi$ coupling by assuming universal coupling of the $\rho$ to the isospin current. The resulting theoretical cross section is found to be too small by roughly a factor of six at 910 MeV/c and in rough agreement within theoretical uncertainties at 1.4 BeV/c and 1.96 BeV/c if the effect of the form factor in reducing the cross section is taken into account. Formulas for the decay of an arbitrary isobar excited by spin-1 exchange and a test for spin-1 exchange are given. In the Appendices, production of ${\omega }^0$ with $N^{*}$ is discussed and a brief treatment in terms of $N^{*}$ as a spin-$\frac{3}{2}$ particle is given.