Study of light $\varphi$-mesic nuclei with HAL QCD $\varphi N$ interactions

Abstract

We explore the possible existence of light $\varphi$-mesic nuclei using HAL QCD $\varphi N$ interactions for the ${}^2{S}_{1/2}$ and ${}^4{S}_{3/2}$ channels. Particularly, using the Faddeev formalism in configuration space, the $\varphi NN$ system, and ${}_{\varphi }^9$Be and ${}_{\varphi \varphi }^6$He nuclei within the framework of the three-body cluster model, are investigated. The $\varphi \alpha$ effective potential, obtained through a folding procedure, involves the HAL QCD $\varphi N$ interaction in the ${}^4{S}_{3/2}$ channel which does not lead to a bound state of the $\varphi N$ pair while the $\varphi N$ ${}^2{S}_{1/2}$ channel yields the bound state as the ${}_{\varphi }^3$H nucleus. The ${}^4{S}_{3/2}$ potential ensures that the folding procedure is appropriate because there are no open channels like $\varphi +N$ and $\varphi +2N$ near or below the $\varphi +4N$ threshold, and it utilizes different matter distributions of ${}^4$He proposed in the literature. The folding potential is approximated by the Woods-Saxon formula. The mirror systems $\varphi$+$\alpha$+$\alpha$ and $\varphi$+$\varphi$+$\alpha$ have energy ranges from 1-11 MeV and 3-10~MeV, respectively. The predicted binding energies represent the minimal values for the hypothetical $\varphi$ mesic nuclei ${}_{\varphi }^5$He, ${}_{\varphi }^9$Be and ${}_{\varphi \varphi }^6$He. The phenomenological $\alpha \alpha$ and $\varphi \varphi$ potentials are adopted from the literature.

Comments: 19 pages,6 figures. arXiv admin note: substantial text overlap with arXiv:2408.13415, arXiv:2407.12190