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

TL;DR

This study explores the possibility of a $^{3}_{\phi}$H hypernucleus using HAL QCD potentials, finding potential bound states depending on interaction channels and parameters, thus contributing to understanding hypernuclear systems.

Contribution

The paper applies the Faddeev formalism with HAL QCD potentials to predict bound states in the $\phi NN$ system, highlighting the sensitivity to interaction parameters and confirming previous predictions.

Findings

Bound state in $^3_\phi$H with 14.9 MeV binding energy at specific parameters.

Confirmation of bound states in $\phi NN$ systems with Yukawa-type potentials.

Binding energies for different spin-isospin configurations vary significantly.

Abstract

Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the $\phi NN$ system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD $\phi N$ potential in the $^{4}S_{3/2}$ channel does not support either $\phi N$ or $\phi NN$ bound states. The HAL QCD $\phi N$ potential in the $^{2}S_{1/2}$ channel suggests the bound states for $\phi N$ and $\phi NN (S=0)$ systems. However, the binding energies are highly sensitive to variations of the enhancement factor $\beta$, and the $\phi NN$ system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential %$(\frac{1}{3}V_{\phi N}^{1/2}+\frac{2}{3}V_{\phi N}^{3/2})$ for the state $S=1$ yields a bound state for $^3_\phi$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 $\phi NN$ ($S=2,T=0$ 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.