Extended-soft-core baryon-baryon model. II. Hyperon-nucleon interaction

The YN results are presented from the extended soft-core (ESC) interactions. They consist of local and nonlocal potentials because of (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial mesons; (ii) diffractive exchanges; (iii) two-pseudoscalar exchange; and (iv) meson-pair exchange (MPE). Both the OBE and pair vertices are regulated by Gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices is dependent on the SU(3) classification of the exchanged mesons for OBE and a similar scheme for MPE. The particular version of the ESC model, called ESC04 [T. A. Rijken, Phys. Rev. C 73, 044007 (2006)], describes nucleon-nucleon (NN) and hyperon-nucleon (YN) interactions in a unified way using broken SU(3) symmetry. Novel ingredients are the inclusion of (i) the axial-vector meson potentials and (ii) a zero in the scalar- and axial-vector meson form factors. These innovations made it possible for the first time to keep the parameters of the model close to the predictions of the ${}^3{P}_0$ quark-antiquark creation model. This is also the case for the $F/(F+D)$ ratios. Furthermore, the introduction of the zero helped to avoid the occurrence of unwanted bound states. Broken SU(3) symmetry serves to connect the NN and the YN channels, which leaves after fitting NN only a few free parameters for the determination of the YN interactions. In particular, the meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the NN analysis as input. Here, as a novel feature, medium-strong flavor-symmetry breaking (FSB) of the coupling constants was allowed, using the ${}^3{P}_0$ model with a Gell-Mann-Okubo hypercharge breaking for the BBM coupling. Very good fits for ESC model with and without FSB were obtained. The charge-symmetry breaking in the $\Lambda p$ and $\Lambda n$ channels, which is an SU(2) isospin breaking, is included in the OBE, TME, and MPE potentials. Simultaneous fits to the NN- and the YN-scattering data are described, using different options for the ESC model. For the selected 4233 NN data with energies $0\le T_{\mathrm{lab}}\le 350$ MeV, a ${\chi }^2/N_{\mathrm{data}}=1.22$ was typically reached. For the usual set of 35 YN data and 3 ${\Sigma }^{+}p$ cross sections from a recent KEK experiment E289 ${\chi }^2/{\mathit{YN}}_{\mathrm{data}}\approx 0.63$ was obtained. In particular, we were able to fit the precise experimental datum $r_R=0.468\pm 0.010$ for the inelastic capture ratio at rest rather well. The four versions (a,b,c, and d) of ESC04 presented in this article, give different results for hypernuclei. The reported G-matrix calculations are performed for YN ($\Lambda N,\Sigma N,\Xi N$) pairs in nuclear matter. The obtained well depths ($U_{\Lambda },U_{\Sigma },U_{\Xi }$) reveal distinct features of ESC04a–d. The $\Lambda \Lambda$ interactions are demonstrated to be consistent with the observed data of ${}_{\Lambda \Lambda }^6$He. The possible three-body effects are investigated by considering phenomenologically the changes of the vector-meson masses.

Figure 1

Octet representation indices OBE graphs. The solid lines denote baryons with labels $i,m,j,n$. The dashed line with label p refers to the bosons: pseudoscalar, vector, axial-vector, or scalar mesons.

Figure 2

Octet representation indices TME parallel graphs. The solid lines denote baryons with labels $i,m,j,n,r,s$. The dashed lines with labels $p,q$ refer to the pseudoscalar mesons.

Figure 3

Octet representation indices TME crossed graphs. The solid lines denote baryons with labels $i,m,j,n,r,s$. The dashed lines with labels p and q refer to the pseudoscalar mesons.

Figure 4

Octet representation indices MPE one-pair graphs. The solid lines denote baryons with labels $i,m,j,n,s$. The dashed lines with labels p and q refer to the pseudoscalar, etc., mesons.

Figure 5

Octet representation indices MPE two-pair graphs. The solid lines denote baryons with labels $i,m,j,n$. The dashed lines with labels p and q refer to the pseudoscalar, etc., mesons.

Figure 6

Total potentials in the partial waves ${}^1{S}_0$ and ${}^3{S}_1$, for the $I=1/2$ and $I=3/2$ states.

Figure 7

OBE potentials in the partial waves ${}^1{S}_0$ and ${}^3{S}_1$, for the $I=1/2$ and $I=3/2$ states.

Figure 8

TPS potentials in the partial waves ${}^1{S}_0$ and ${}^3{S}_1$, for the $I=1/2$ and $I=3/2$ states.

Figure 9

Pair potentials in the partial waves ${}^1{S}_0$ and ${}^3{S}_1$, for the $I=1/2$ and $I=3/2$ states.

Figure 10

OBE potentials in the ${}^1{S}_0$ partial waves, for pseudoscalar (PS), vector (VC), scalar (SC), and axial-vector (AX) exchange, in the $I=1/2$ and $I=3/2$ states.

Figure 11

OBE potentials in the ${}^3{S}_1$ partial waves, for pseudoscalar (PS), vector (VC), scalar (SC), and axial-vector (AX) exchange, in the $I=1/2$ and $I=3/2$ states.

Figure 12

Calculated values of $U_{\Lambda }$ as a function of $\rho /{\rho }_0$ for ESC04a (solid curve), ESC04b (dashed curve), ESC04c (dotted curve), and ESC04d (dot-dashed curve). The thin dashed curve is for NSC97f.

Figure 13

S- and P-state contributions to $U_{\Lambda }$ are shown in the left and right panels, respectively, as a function of $\rho /{\rho }_0$. The solid, dashed, dotted, and dot-dashed curves are for ESC04a–d, respectively. The thin dashed curve is for NSC97f.

Figure 14

Calculated values of $m_{\Lambda }^{*}$ as a function of $\rho /{\rho }_0$ for ESC04a (solid curve), ESC04b (dashed curve), ESC04c (dotted curve), and ESC04d (dot-dashed curve). The thin dashed curve is for NSC97f.

Figure 15

Triple-meson three-body interaction.

Figure 16

Binding energy per nucleon $B/A$ in symmetric nuclear matter as a function of $\rho /{\rho }_0$ (saturation curve). The box represents the area in which saturation occurs empirically. (Left panel) The two solid curves show the G-matrix results for ESC04 (NN) with the QTQ and CIES prescriptions. (Right panel) The dashed curves are obtained by adding the TNI contributions on the QTQ result, and the solid curves are for the medium-corrected versions ESC04${}^{*}$ (NN). See the text for the detail.

Figure 17

Calculated values of $U_{\Lambda }$ as a function of $\rho /{\rho }_0$. The three solid curves are for ESC04b, ESC04b${}^{*}({\alpha }_V=0.07)$, and ESC04b${}^{*}({\alpha }_V=0.18)$. The two dashed curves are obtained by adding the TNR2 and TNR3 contributions on the result for ESC04b. See the text for the detail.