Dynamical coupled-channel model of kaon-hyperon interactions

The $\pi N\to KY$ and $KY\to KY$ reactions are studied using a dynamical coupled-channel model of meson-baryon interactions at energies where the baryon resonances are strongly excited. The channels included are: $\pi N$, $K\Lambda$, and $K\Sigma$. The resonances considered are: $N^{*}\left[S_{11}\left(1650\right),P_{11}\left(1710\right),P_{13}\left(1720\right),D_{13}\left(1700\right)\right]$; ${\Delta }^{*}\left[S_{31}\left(1900\right),P_{31}\left(1910\right),P_{33}\left(1920\right)\right]$; ${\Lambda }^{*}\left[S_{01}\left(1670\right),P_{01}\left(1810\right)\right]$ ${\Sigma }^{*}\left[P_{11}\left(1660\right),D_{13}\left(1670\right)\right]$; and $K^{*}\left(892\right)$. The basic nonresonant $\pi N\to KY$ and $KY\to KY$ transition potentials are derived from effective Lagrangians using a unitary transformation method. The dynamical coupled-channel equations are simplified by parametrizing the $\pi N\to \pi N$ amplitudes in terms of empirical $\pi N$ partial-wave amplitudes and a phenomenological off-shell function. Two models have been constructed. Model $\mathrm{A}$ is built by fixing all coupling constants and resonance parameters using $\mathrm{SU}\left(3\right)$ symmetry, the Particle Data Group values, and results from a constituent quark model. Model $\mathrm{B}$ is obtained by allowing most of the parameters to vary around the values of model $\mathrm{A}$ in fitting the data. Good fits to the available data for ${\pi }^{-}p\to K^0\Lambda ,K^0{\Sigma }^0$ have been achieved. The investigated kinematics region in the center-of-mass frame goes from threshold to $2.5\mathrm{GeV}$. The constructed models can be imbedded into associated dynamical coupled-channel studies of kaon photo- and electroproduction reactions.

Figure 1

Graphical representation for $\sigma$-exchange $\pi N$ interaction.

Figure 2

Graphical representation of the potentials in $\pi N\to KY$, (a) direct nucleon pole $v_{N_D}$, (b) hyperon exchange $v_{Y_E}$, (c) strange vector meson exchange $v_{K^{*}}$, and (d) hyperon resonance exchange $v_{Y_E^{*}}$.

Figure 3

Graphical representation of the potentials in $KY\to KY$, (a) direct nucleon pole $v_{N_D}$, (b) $\Xi$ exchange $v_{{\Xi }_E}$, (c) vector meson exchange $v_{\rho }$, and (d) $\Xi$ resonance exchange $v_{{\Xi }_E^{*}}$.

Figure 4

Differential cross section for the reaction ${\pi }^{-}p\to K^{\circ }\Lambda$. The curves are from models $\mathrm{A}$ (dashed curves) and $\mathrm{B}$ (full curves). Data are from Refs. 27, 29.

Figure 5

Differential cross section for the reaction ${\pi }^{-}p\to K^{\circ }{\Sigma }^{\circ }$. The curves are as in Fig. 4. Data are from Refs. 28, 31.

Figure 6

$\Lambda$-polarization asymmetries for the reaction ${\pi }^{-}p\to K^{\circ }\Lambda$. The curves are as in Fig. 4. Data are from Refs. 27, 30.

Figure 7

$\Sigma$-polarization asymmetries for the reaction ${\pi }^{-}p\to K^{\circ }{\Sigma }^{\circ }$. The curves are as in Fig. 4. Data are from Ref. 31.

Figure 8

Excitation function at three angles for the reaction ${\pi }^{-}p\to K^{\circ }\Lambda$ from threshold up to $W=2.3\mathrm{GeV}$. The curves are from model $\mathrm{B}$ (full curve), and the same model without one nucleon resonance: $N4$ (dotted), $N5$ (dashed), $N6$ (long dashed), and $N7$ (dash-dotted).

Figure 9

Same as Fig. 8, but for the ${\pi }^{-}p\to K^{\circ }{\Sigma }^{\circ }$ channel.

Figure 10

Total cross section for the reactions ${\pi }^{-}p\to K^{\circ }\Lambda$ (upper box), and ${\pi }^{-}p\to K^{\circ }{\Sigma }^{\circ }$ (lower box). Curves are the same as in Fig. 4. Data are from Refs. 27, 29, 30, 31.

Figure 11

Total cross section for the reactions $K^{\circ }\Lambda \to K^{\circ }\Lambda$ (upper box), $K^{\circ }\Lambda \to K^{\circ }{\Sigma }^{\circ }$ (middle box), and $K^{\circ }{\Sigma }^{\circ }\to K^{\circ }{\Sigma }^{\circ }$ (lower box). Curves come from only resonant terms for models $\mathrm{A}$ and $\mathrm{B}$ (dotted and dash-dotted, respectively, and full $\mathrm{A}$ and $\mathrm{B}$ models (dashed and full curves, respectively).