Constraining hypernuclear density functional with $Λ$-hypernuclei and compact stars

We present a simultaneous calculation of heavy single-$Λ$ hypernuclei and compact stars containing hypernuclear core within a relativistic density functional theory based on a Lagrangian which includes the hyperon octet and lightest isoscalar-isovector mesons which couple to baryons with density-dependent couplings. The corresponding density functional allows for SU(6) symmetry breaking and mixing in the isoscalar sector, whereby the departures in the $σ$-$Λ$ and $σ$-$Σ$ couplings away from their values implied by the SU(3) symmetric model are used to adjust the theory to the laboratory and astronomical data. We fix $σ$-$Λ$ coupling using the data on the single-$Λ$ hypernuclei and derive an upper bound on the $σ$-$Σ$ from the requirement that the lower bound on the maximum mass of a compact star is $2 M_{\odot}$.

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