Predictions for charmed nuclei based on $Y_c N$ forces inferred from lattice QCD simulations

Charmed nuclei are investigated utilizing $Λ_c N$ and $Σ_c N$ interactions that have been extrapolated from lattice QCD simulations at unphysical masses of $m_π= 410$--$570$ MeV to the physical point using chiral effective field theory as guideline. Calculations of the energies of $Λ_c$ single-particle bound states for various charmed nuclei from $^{\ 5}_{Λ_c}$Li to $^{209}_{Λ_c}$Bi are performed using a perturbative many-body approach. This approach allows one to determine the finite nuclei $Λ_c$ self-energy from which the energies of the different bound states can be obtained. Though the $Λ_c N$ interaction inferred from the lattice results is only moderately attractive, it supports the existence of charmed nuclei. Already the lightest nucleus considered is found to be bound. The spin-orbit splitting of the p- and d-wave states turns out to be small, as in the case of single $Λ$ hypernuclei. Additional calculations based on the Faddeev-Yakubovsky equations suggest that also $A=4$ systems involving a $Λ_c$ baryon are likely to be bound, but exclude a bound $^{\, 3}_{Λ_c}$He state.

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