Soft-core hyperon-nucleon potentials

Abstract

A new Nijmegen soft-core OBE potential model is presented for the low-energy 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. An important innovation with respect to the original soft-core potential is the assignment of the cut-off masses for the baryon-baryon-meson (BBM) vertices in accordance with broken SU(3)$_F$, which serves to connect the NN and the YN channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the $^3P_0$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. We present six hyperon-nucleon potentials which describe the available 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 $\Sigma N$ and $\Lambda N$ channels. For the scalar-meson mixing angle we obtained values $\theta_S=37$ to 40 degrees, which points to almost ideal mixing angles for the scalar $q\bar{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\Lambda$ hypernuclei.Comment: 37 pages, 4 figure

Hyperon–nucleon interactions—a chiral effective field theory approach

“…The differential cross sections at low energies, which have not been taken into account in the fitting procedure, are predicted well, see The Λp and Σ + p scattering lengths and effective ranges are listed in Table 4.3 together with the corresponding hypertriton binding energies (preliminary results of Y NN Faddeev calculations from [35]). The magnitudes of the Λp singlet and triplet scattering lengths are smaller than the corresponding values of the Nijmegen NSC97e,f and Jülich '04 models [19,24], which is also reflected in the small Λp cross section near threshold, see Figure 4.1a. The mentioned models lead to a bound hypertriton [35,36].…”

“…This explains why the chiral EFT phase shifts are quite different from the phase shifts of the models presented in Refs. [19,24]. Actually, the predictions of the latter models also differ between each other in many partial waves.…”

“…The mentioned models lead to a bound hypertriton [35,36]. Although our Λp scattering lengths differ significantly from those of [19,24], the Y N interaction based on chiral EFT also yields a correctly bound hypertriton, see Table 4.3. Our singlet Σ + p scattering length is about half as large as the values found for the Y N potentials in [19,24].…”

“…These data have also been used in [19,24] and are listed in Table 4.2 (see below). The higher energy total cross sections and differential cross sections are then predictions of the LO chiral EFT, which contains five free parameters.…”

“…Following [24], we use cos θ min = −0.5 and cos θ max = 0.5 in our calculations for the Σ + p → Σ + p and Σ − p → Σ − p cross sections, in order to stay as close as possible to the experimental procedure.…”