Dynamical coupled-channels approach to hadronic and electromagnetic kaon-hyperon production on the proton

A dynamical coupled-channels formalism for processes $\pi N\to \mathit{KY}$ and $\gamma N\to \mathit{KY}$ is presented that provides a comprehensive investigation of recent data on the $\gamma p\to K^{+}\Lambda$ reaction. The nonresonant interactions within the subspace $\mathit{KY}\oplus \pi N$ are derived from effective Lagrangians, using a unitary transformation method. The calculations of photoproduction amplitudes are simplified by casting the coupled-channels equations into a form such that the empirical $\gamma N\to \pi N$ amplitudes are input and only the parameters associated with the $\mathit{KY}$ channel are determined by performing ${\chi }^2$ fits to all of the available data for ${\pi }^{-}p\to K^{°}\Lambda ,K^{°}{\Sigma }^{°}$, and $\gamma p\to K^{+}\Lambda$. Good agreement between our models and those data are obtained. In the fits to $\pi N\to \mathit{KY}$ channels, most of the parameters are constrained within $\pm 20\%$ of the values given by the Particle Data Group and/or quark model predictions, whereas for $\gamma p\to K^{+}\Lambda$ parameters, ranges compatible with broken SU(6) ⊗ O(3) symmetry are imposed. The main reaction mechanisms in $K^{+}\Lambda$ photoproduction are singled out and issues related to newly suggested resonances $S_{11},P_{13}$, and $D_{13}$ are studied. Results illustrating the importance of using a coupled-channels treatment are reported. Meson cloud effects on the $\gamma N\to N^{*}$ transitions are also discussed.

Figure 1

Differential cross section for the reaction ${\pi }^{-}p\to K^{°}\Lambda$. The solid curves are from the fits using the coupled-channels model of this work. Data are from Refs. 53, 55.

Figure 2

Differential cross section for the reaction ${\pi }^{-}p\to K^{°}{\Sigma }^{°}$. The solid curves are from the fits using the coupled-channels model of this work. Data are from Refs. 54, 57.

Figure 3

Λ recoil polarization asymmetries for the reaction ${\pi }^{-}p\to K^{°}\overrightarrow{\Lambda }$. The solid curves are from the fits using the coupled-channels model of this work. Data are from Refs. 53, 56.

Figure 4

Σ recoil polarization asymmetries for the reaction ${\pi }^{-}p\to K^{°}{\overrightarrow{\Sigma }}^{°}$. The solid curves are from the fits using the coupled-channels model of this work. Data are from Ref. 57.

Figure 5

Differential cross section for the reaction $\gamma p\to K^{+}\Lambda$ as a function of total-center-of-mass energy. Dotted and solid curves correspond to models $M_1$ and $M_2$ respectively. Data are from Ref. 1 (open diamonds), Ref. 3 (full circles), and LEPS [6] (open squares in the cells corresponding to cos $\theta =0.75$ and 0.85). Plotted data from Ref. 1 are measured at $\cos (\theta ){}^{\text{'}}=\cos (\theta )+0.05$.

Figure 6

Angular distribution for recoil Λ polarization asymmetry for the reaction $\gamma p\to K^{+}\overrightarrow{\Lambda }$. Curves as in Fig. 5. Data are from Ref. 2.

Figure 7

Angular distribution for polarized beam asymmetry for the reaction $\overrightarrow{\gamma }p\to K^{+}\Lambda$. Curves as in Fig. 5. Data are from Ref. 5 (circles) and Ref. 6 (squares).

Figure 8

Excitation function for polarized target asymmetry for the reaction $\gamma \overrightarrow{p}\to K^{+}\Lambda$. Curves as in Fig. 5. Data are from Ref. 61.

Figure 9

Differential cross section for the reaction $\gamma p\to K^{+}\Lambda$ as a function of total-center-of-mass energy. Solid curve corresponds to the full model $M_2$. Dotted, dot-dashed, and dashed curves correspond to the full model without the third $S_{11}$, third $P_{13}$, and third $D_{13}$, respectively. Data are as in Fig. 5

Figure 10

Angular distribution for recoil Λ polarization asymmetry for the reaction $\gamma p\to K^{+}\overrightarrow{\Lambda }$. Curves as described in the legend to Fig. 9. Data are from Ref. 2.

Figure 11

Angular distribution for polarized beam asymmetry for the reaction $\overrightarrow{\gamma }p\to K^{+}\Lambda$. Curves as described in the legend to Fig. 9. Data are from Ref. 5.

Figure 12

Excitation function for polarized target asymmetry for the reaction $\gamma \overrightarrow{p}\to K^{+}\Lambda$. Curves as described in the legend to Fig. 9. Data are from Ref. 61.

Figure 13

Total cross section for $\gamma p\to K^{+}\Lambda$ as a function of total center-of-mass energy. The bold full curves come from the model $M_2$. In each cell different curves correspond to the model $M_2$ with one resonance switched off, as singled out in each cell. Data are from Refs. 1, 3.

Figure 14

Differential cross section excitation functions at four angles for $\gamma p\to K^{+}\Lambda$. The curves are as follows: model $M_2$ (full curves), direct-channel results obtained by turning off multistep processes in the full calculation (dotted curves), and off-shell effects swithed off in the full calculation (dashed curves). Data as in Fig. 5.

Figure 15

The multipole amplitudes calculated from the $\gamma N\to N^{*}\to \mathit{KY}$ resonant transition for each of the three considered $S_{11}$-, $P_{13}$-, and $D_{13}$-wave resonances. The curves are as follows: model $M_2$ (full) and the meson cloud effect Eq. (9) turned off (dotted). The dashed curves correspond to the relevant third resonances switched off: $S_{11}$(1806) in $E_0^{+},P_{13}$(1893) in $E_1^{+}$ and $M_1^{+}$, and $D_{13}$(1954) in $E_2^{-}$ and $M_2^{-}$.