On a possible ${}_{\varphi }^3$H hypernucleus with HAL QCD interaction

Abstract

Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the $\varphi NN$ system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD $\varphi N$ potential in the ${}^4{S}_{3/2}$ channel does not support either $\varphi N$ or $\varphi NN$ bound states. The HAL QCD $\varphi N$ potential in the ${}^2{S}_{1/2}$ channel suggests the bound states for $\varphi N$ and $\varphi NN(S=0)$ systems. However, the binding energies are highly sensitive to variations of the enhancement factor $\beta$, and the $\varphi NN$ system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential %$(\frac{1}{3}{V}_{\varphi N}^{1/2}+\frac{2}{3}{V}_{\varphi N}^{3/2})$ for the state $S=1$ yields a bound state for ${}_{\varphi }^3$H $(S=1)$ hypernucleus with the binding energy (BE) 14.9 MeV when $\beta =6.9$. The evaluation of the BE for the $S=1$, $T=1$ three-body state results in 5.47 MeV. %Also, We evaluated the BE for the $S=1$, $T=1$ three-body state as 5.47 MeV. Additionally, calculations using our approach confirm the bound states for the $\varphi NN$ ($S=2,T=0$ and $S=1,T=1$) system previously predicted with the Yukawa-type potential motivated by the QCD van der Waals attractive force, mediated by multi-gluon exchanges.

arXiv comment6 Pages, 1 figure

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• Examination of the lattice QCD-motivated strong attractive $\Omega N$ potentials in the ${\Omega }^{-}np$ system
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