Baryon-Baryon Interactions

We review the Nijmegen extended-soft-core (ESC) models for the baryon-baryon (BB) interactions of the SU(3) flavor-octet of baryons (N, Λ, Σ, and Ξ). The interactions are basically studied from the meson-exchange point of view, in the spirit of the Yukawa-approach to the nuclear force problem [H. Yukawa, “On the interaction of Elementary Particles I”, Proceedings of the Physico-Mathematical Society of Japan 17 (1935), 48], using generalized soft-core Yukawa-functions. These interactions are supplemented with (i) multiple-gluon-exchange, and (ii) structural effects due to the quark-core of the baryons. We present in some detail the most recent extended-soft-core model, henceforth referred to as ESC08, which is the most complete, sophisticated, and successful interaction-model. Furthermore, we discuss briefly its predecessor the ESC04-model [Th. A. Rijken and Y. Yamamoto, Phys. Rev. C 73 (2006), 044007; Th. A. Rijken and Y. Yamamoto, Phys. Rev. C 73 (2006), 044008; Th. A. Rijken and Y. Yamamoto, nucl-th/0608074]. For the soft-core one-boson-exchange (OBE) models we refer to the literature [Th. A. Rijken, in Proceedings of the International Conference on Few-Body Problems in Nuclear and Particle Physics, Quebec, 1974, ed. R. J. Slobodrian, B. Cuec and R. Ramavataram (Presses Universitè Laval, Quebec, 1975), p. 136; Th. A. Rijken, Ph. D. thesis, University of Nijmegen, 1975; M. M. Nagels, Th. A. Rijken and J. J. de Swart, Phys. Rev. D 17 (1978), 768; P. M. M. Maessen, Th. A. Rijken and J. J. de Swart, Phys. Rev. C 40 (1989), 2226; Th. A. Rijken, V. G. J. Stoks and Y. Yamamoto, Phys. Rev. C 59 (1999), 21; V. G. J. Stoks and Th. A. Rijken, Phys. Rev. C 59 (1999), 3009]. All ingredients of these latter models are also part of ESC08, and so a description of ESC08 comprises all models so far in principle. The extended-soft-core (ESC) interactions consist of local- and non-local-potentials due to (i) one-boson-exchanges (OBE), which are the members of nonets of pseudo-scalar-, vector-, scalar-, and axial-mesons, (ii) diffractive (i.e. multiple-gluon) exchanges, (iii) two pseudo-scalar exchange (PS-PS), and (iv) meson-pair-exchange (MPE). The OBE- and pairvertices are regulated by gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cutoff masses for the BBM-vertices is dependent on the SU(3)-classification of the exchanged mesons for OBE, and a similar scheme for MPE. The ESC-models ESC04 and ESC08 describe the nucleon-nucleon (NN), hyperonnucleon (YN), and hyperon-hyperon (YY) interactions in a unified way using broken SU(3)-symmetry. Novel ingredients in the OBE-sector in the ESC-models are the inclusion of (i) the axial-vector meson potentials, (ii) a zero in the scalar- and axial-vector meson form factors. These innovations made it possible for the first time to keep the meson coupling parameters of the model qualitatively in accordance with the predictions of the 3P0 quark-antiquark creation (QPC) 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 in ΛN. 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 ⊕ YN-analysis as input. In ESC04 medium strong flavor-symmetry-breaking (FSB) of the coupling constants was investigated, using the 3P0-model with a Gell-Mann-Okubo hypercharge breaking for the BBM-coupling. In ESC08 the couplings are kept SU(3)-symmetric. The charge-symmetry-breaking (CSB) in the Λp and Λn channels, which is an SU(2) isospin breaking, is included in the OBE-, TME-, and MPE-potentials. In ESC04 and ESC08 simultaneous fits to the NN- and the YN-scattering data have been achieved, using different options for the ESC-model. In particularly in ESC08 with single-sets of parameters excellent fits were obtained for the NN- and YN-data. For example, in the case of ESC08a' we have: (i) For the selected 4233 NN-data with energies 0 ≤ Tlab ≤ 350 MeV, excellent results were obtained having χ2/Ndata = 1.094. (ii) For the usual set of 35 Y N-data and 3 Σ+p cross-sections from a recent KEK-experiment E289 [H. Kanda et al., AIP Conf. Proc. 842 (2006), 501; H. Kanda, Measurement of the cross sections of Σ=p elastic scattering, Ph. D. thesis, Department of Physics, Faculty of Science, Kyoto University, March 2007] the fit has χ2/YNdata ≈ 0.83. (iii) For Y Y there is a weak ΛΛ-interaction, which successfully matches with the Nagara-event [H. Takahashi et al., Phys. Rev. Lett. 87 (2001), 212502]. (iv) The nuclear Σ and Ξ well-dephts satisfy UΣ > 0 and UΞ < 0. The predictions for the S = −2 (ΛΛ, ΞN, ΛΣ, ΣΣ)-channels are the occurrences of an S = −2 bound states in the ΞN(3S1 − 3D1, I = 0, 1)-channels.

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