Properties of charmed and bottom hadrons in nuclear medium: Results for $\Lambda_c^+$ and $\Lambda_b$ hypernuclei

This reports our recent studies on changes in properties of heavy hadrons containing at least a charm or a bottom quark in nuclear matter, and that the results for the $\Lambda^+_c$ and $\Lambda_b$ hypernuclei are studied quantitatively. Comparisons are made with the results for the $\Lambda$ hypernuclei studied previously in the same approach. It is shown that although the scalar and vector potentials for the $\Lambda$, $\Lambda_c^+$ and $\Lambda_b$ in the hypernuclei multiplet with the same baryon numbers are quite similar, the wave functions obtained, e.g., for $1s_{1/2}$ state, are very different. The $\Lambda^+_c$ probability density distribution in $^{209}_{\Lambda^+_c}$Pb is much more pushed away from the center than that for the $\Lambda$ in $^{209}_\Lambda$Pb due to the Coulomb force. On the contrary, the $\Lambda_b$ probability density distributions in $\Lambda_b$ hypernuclei are much larger near the origin than those for the $\Lambda$ in the $\Lambda$ hypernuclei due to its heavy mass. A possibility of $B^-$ nuclear bound (atomic) states is also briefly discussed.