Possible <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mprescripts/> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:mrow> </mml:math> hypernucleus with the HAL QCD interaction
Igor Filikhin, Roman Ya. Kezerashvili, Branislav Vlahović
Abstract
Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the $\ensuremath{\phi}NN$ system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD $\ensuremath{\phi}N$ potential in the ${^{4}S}_{3/2}$ channel does not support either $\ensuremath{\phi}N$ or $\ensuremath{\phi}NN$ bound states. The HAL QCD $\ensuremath{\phi}N$ potential in the ${^{2}S}_{1/2}$ channel suggests the bound states for $\ensuremath{\phi}N$ and $\ensuremath{\phi}NN(S=0)$ systems. However, the binding energies are highly sensitive to variations of the enhancement factor $\ensuremath{\beta}$, and the $\ensuremath{\phi}NN$ system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential for the state $S=1$ yields a bound state for the $_{\ensuremath{\phi}}^{3}\mathrm{H}$ ($S=1$) hypernucleus with the binding energy (BE) 14.9 MeV when $\ensuremath{\beta}=6.9$. The evaluation of the BE for the $S=1$, $T=1$ three-body state results in 5.47 MeV. Additionally, calculations using our approach confirm the bound states for the $\ensuremath{\phi}NN$ ($S=2$, $T=0$ and $S=1$, $T=1$) system previously predicted with the Yukawa-type potential motivated by the QCD van der Waals attractive force, mediated by multigluon exchanges.