Jülich hyperon-nucleon model revisited

A one-boson-exchange model for the hyperon-nucleon ($\Lambda N,\Sigma N$) interaction is presented. The model incorporates the standard one boson exchanges of the lowest pseudoscalar and vector meson multiplets with coupling constants fixed by SU(6) flavor symmetry relations. As the main new feature of the model, the contributions in the scalar-isoscalar (σ) and vector-isovector (ρ) exchange channels are now constrained by a microscopic model of correlated $\pi \pi$ and $K\overline{K}$ exchange. Additional short-ranged ingredients of the model in the scalar-isovector ($a_0$) and scalar-isospin-1/2 (κ) channels are likewise viewed as arising from meson-meson correlations but are treated phenomenologically. With this model a satisfactory reproduction of the available hyperon-nucleon data can be achieved.

Figure 1

Two-pion exchange in the NN interaction: (a) uncorrelated iterative and (b) crossed boxes, (c) correlated two-pion exchange.

Figure 2

The dynamical model for the $B\overline{B}\to \mu \overline{\mu }$ amplitude ($\mu \overline{\mu }=\pi \pi ,K\overline{K}$).

Figure 3

The contributions to the potential of the coupled channel $\pi \pi -K\overline{K}$ model of Ref. 18.

Figure 4

The contributions to the Born amplitude for the transitions $\Sigma \overline{\Sigma }\to \pi \pi ,K\overline{K}$.

Figure 5

The σ-like part of the $\Lambda N$ and $\Sigma N$ on-shell potentials in the ${}^1{S}_0$ partial wave. The solid lines are derived from our microscopic model of correlated $\pi \pi$ and $K\overline{K}$ exchange. The dotted lines are obtained if the dispersion-theoretical result is parametrized by σ exchange, while the dashed lines correspond to the σ exchange used in the Jülich YN potential A [1].

Figure 6

Contributions to the interaction in the (a) $\Lambda N$ and (b) $\Sigma N$ channels and in the (c) $\Lambda N\to \Sigma N$ transition. Note that only $\pi ,K,\omega$, and $K^{*}$ exchange are considered as being due to genuine SU(3) mesons. The other contributions are either fixed from correlated $\pi \pi$ and $K\overline{K}$ exchange ($\sigma ,\rho$) or are viewed as an effective parametrization of meson-meson correlations ($a_0,\kappa ,{\omega }^{\text{'}}$) in the corresponding spin-isospin channels.

Figure 7

(Color online) Total YN scattering cross sections as a function of the laboratory momentum. The solid lines are results of the new YN model, based on correlated $\pi \pi$ and $K\overline{K}$ exchange, while the dash-dotted lines are results of the Jülich YN model A [1]. The dashed lines are results of an alternative model where κ exchange is replaced by a contact term, cf. text. The data are from Refs. 30, 31, 32, 33, 34.

Figure 8

(Color online) Total YN scattering cross sections as a function of the laboratory momentum. Comparison with data at higher energies. Same description of curves as in Fig. 7. The data are from Refs. 35, 36.

Figure 9

(Color online) Differential YN scattering cross sections at selected laboratory momenta where data are available. Same description of curves as in Fig. 7. The data are from Refs. 33, 34, 36, 37.

Figure 10

(Color online) Some differential observables for the reaction $\Lambda N$ at the laboratory momenta 150 and 600 MeV/c. Same description of curves as in Fig. 7.

Figure 11

(Color online) Differential cross sections and polarizations for the reactions $\Sigma N$ at the laboratory momentum 500 MeV/c. Same description of curves as in Fig. 7.

Figure 12

(Color online) Phase shifts for selected $\Lambda N$ and $\Sigma N$ S and D waves as a function of the laboratory energy. Same description of curves as in Fig. 7.

Figure 13

(Color online) Phase shifts for $\Lambda N$ and $\Sigma N$ P waves as a function of the laboratory energy. The left panel shows results of our new YN model and the right panel those of the original Jülich YN model A [1].