Twelve-quark hypernuclei with A=4 in relativistic quark-gluon model

Abstract

Hypernuclei $ ^4_Y He$, $ ^4_Y H$, $ ^4_{YY} He$, $ ^4_{YY} H$, where $Y=Λ$, $Σ_0$, $Σ_+$, $Σ_-$, A=4 are considered using the relativistic twelve-quark equations in the framework of the dispersion relation technique. Hypernuclei as the systems of interacting quarks and gluons are considered. The relativistic twelve-quark amplitudes of hypernuclei, including $u$, $d$, $s$ quarks are constructed. The approximate solutions of these equations are obtained using a method based on the extraction of leading singularities of the amplitudes. The poles of the multiquark amplitudes allow us to determine the masses of hypernuclei with the atomic (baryon) number $A=B=4$. The mass of state $ ^4_ΛHe$ with the isospin projection $I_3=1/2$ and the spin-parity $J^P=0^+$ is equal to $M=3922\, MeV$. The mass of $ ^4_{ΛΛ}H$ $M=4118\, MeV$ with the isospin projection $I_3=0$ and the spin-parity $J^P=0^+$ is calculated. We predict the mass spectrum of hypernuclei with A=4, which is valuable to further experimental study of the hypernuclei.