Extended-soft-core baryon-baryon model ESC16. I. Nucleon-nucleon scattering

Abstract

Background: The Nijmegen extended-soft-core (ESC) model ESC16, as well as its predecessors ESC04--ESC08, describe the nucleon-nucleon ($NN$), hyperon-nucleon ($YN$), and hyperon-hyperon/nucleon ($YY/\mathrm{\ensuremath{\Xi}}\phantom{\rule{4pt}{0ex}}N$) interactions in a unified way using broken SU(3) symmetry. SU(3) symmetry serves to connect the $NN$ with the $YN$ and the $YY$ channels. In the spirit of the Yukawa approach to the nuclear force problem, the interactions are studied from the meson-exchange picture viewpoint, using generalized soft-core Yukawa functions. The meson exchanges are supplemented with diffractive contributions due to multiple-gluon exchanges. The extended-soft-core (ESC) meson-exchange interactions consist of local and nonlocal potentials due to (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial-vector mesons, (ii) diffractive exchanges, (iii) two-pseudoscalar exchange (PS-PS), and (iv) meson-pair exchange (MPE). The OBE and MPE vertices 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.Purpose: The evolution of the ESC approach to the ESC16 model for the baryon-baryon (BB) interactions of the SU(3) flavor octet of baryons (N, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Xi}}$) is described and presented. In this first of a series of papers, the $NN$ model and results are reported in detail.Methods: Important nonstandard ingredients in the OBE sector in the ESC models are (i) the axial-vector meson potentials, and (ii) a zero in the scalar- and axial-vector meson form factors. Furthermore, the strange scalar $\ensuremath{\kappa}$ meson is treated within the scheme of the Gell-Mann-Okubo mass relations, and like the $\ensuremath{\rho}$ and $\ensuremath{\epsilon}$ treated as a broad meson. The multiple-gluon exchanges are elaborated further by adding contributions due to odd number of gluon exchanges. A novel contribution is the incorporation of structural effects due to the quark core of the baryons. In establishing the parameters of the model a simultaneous fit to $NN$ and $YN$ channels has been performed. The meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the $NN\ensuremath{\bigoplus}YN$ analysis as input. In ESC16 the couplings are kept completely SU(3) symmetric. About 25 physical coupling parameters and 8 cutoff and diffractive masses were searched.Results: In the fit to $NN$ and $YN$ many parameters are essentially fixed by the $NN$ data. A few, but severely constrained parameters, e.g., $F/(F+D)$ ratios, are left for determination of the $YN$ interactions and the $YY$ experimental indications. The simultaneous fit of the ESC models to the $NN$- and $YN$-scattering data with a single set of parameters has achieved excellent results for the $NN$ and $YN$ data, and for the $YY$ data in accordance with the experimental indications for $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{\ensuremath{\Xi}}N$. In the case of ESC16, the version discussed here, the achievements are: (i) For the selected 4313 $pp$ and $np$ scattering data with energies $0\ensuremath{\le}{T}_{\text{lab}}\ensuremath{\le}350\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, the model reaches a fit having ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.10$. (ii) The deuteron binding energy and all the $NN$ scattering lengths are fitted very nicely. (iii) The $YN$ data are described very well with ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.04$, giving at the same time a description of the $\mathrm{\ensuremath{\Xi}}N$ cross sections in agreement with the experimental indications.Conclusions: The ESC approach leads to an excellent description of the $NN$ and $YN$ data, and for the scarce $YY$ data. The added innovations as well as the treatment of mass broken SU(3) make it possible to keep the meson coupling parameters and the $F/(F+D)$ ratios of the model qualitatively in accordance with the predictions of the $^{3}P_{0}$-dominated quark-antiquark pair creation (QPC) model. The information about estimates of (i) the $\mathrm{\ensuremath{\Lambda}}$- and $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth, and (ii) the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ hypernuclei played an important role in the form of using constraints. In particular, the experimental indications for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$-attraction and the $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth were directive.