Soft-core hyperon-nucleon potentials

Abstract

A new Nijmegen soft-core OBE potential model is presented for the low-energy $\mathrm{YN}$ interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. The potentials are generated by the exchange of nonets of pseudoscalar, vector, and scalar mesons. As is standard in the Nijmegen soft-core models, we also include the $J=0$ contributions from the tensor ${f}_{2}{,f}_{2}^{\ensuremath{'}}{,a}_{2},$ and pomeron Regge trajectories, and use Gaussian form factors to guarantee that the potentials have a soft behavior near the origin. An important innovation with respect to the original soft-core potential is the assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices in accordance with broken $\mathrm{SU}{(3)}_{F},$ which serves to connect the $\mathrm{NN}$ and the $\mathrm{YN}$ channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the ${}^{3}{P}_{0}$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. Charge-symmetry breaking in the $\ensuremath{\Lambda}p$ and $\ensuremath{\Lambda}n$ channels is included as well. We present six hyperon-nucleon potentials which describe the available $\mathrm{YN}$ cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\ensuremath{\Sigma}N$ and $\ensuremath{\Lambda}N$ channels. In all cases, we obtained ${\ensuremath{\chi}}^{2}{/N}_{\mathrm{data}}\ensuremath{\approx}0.55$ for 35 $\mathrm{YN}$ data. In particular, we were able to fit the precise experimental datum ${r}_{R}=0.468\ifmmode\pm\else\textpm\fi{}0.010$ for the inelastic capture ratio at rest. For the scalar-meson mixing angle we obtained values ${\ensuremath{\theta}}_{S}=37\ifmmode^\circ\else\textdegree\fi{}--40\ifmmode^\circ\else\textdegree\fi{},$ which points to almost ideal mixing angles for the scalar $q\overline{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\ensuremath{\Lambda}$ hypernuclei.