Phenomenological view on baryon-baryon potentials from lattice QCD simulations

Abstract

A qualitative discussion on the range of the potentials as they result from the phenomenological meson-exchange picture and from lattice simulations by the HAL QCD Collaboration is presented. For the former pion- and/or $\eta$-meson exchange are considered together with the scalar-isoscalar component of correlated $\pi \pi /K\bar{K}$ exchange. It is observed that the intuitive expectation for the behavior of the baryon-baryon potentials for large separations, associated with the exchange of one and/or two pions, does not always match with the potentials extracted from the lattice simulations. Only in cases where pion exchange provides the longest ranged contribution, like in the $\Xi N$ system, a reasonable qualitative agreement between the phenomenological and the lattice QCD potentials is found for baryon-baryon separations of $r\gtrsim 1$ fm. For the $\Omega N$ and $\Omega \Omega$ interactions where isospin conservation rules out one-pion exchange a large mismatch is observed, with the potentials by the HAL QCD Collaboration being much longer ranged and much stronger at large distances as compared to the phenomenological expectation. This casts some doubts on the applicability of using these potentials in few- or many-body systems.

arXiv comment8 pages, 9 figures

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