${\mathrm{\Lambda }}_{c}N$ interaction from lattice QCD and its application to ${\mathrm{\Lambda }}_c$ hypernuclei

The interaction between ${\mathrm{\Lambda }}_c$ and a nucleon ($N$) is investigated by employing the HAL QCD method in the (2+1)-flavor lattice QCD on a $(2.9\mathrm{f}\mathrm{m}{)}^3$ volume at $m_{\pi }\simeq 410,570,700$ MeV. We study the central potential in ${}^1{S}_0$ channel as well as central and tensor potentials in ${}^3{S}_1-$${}^3{D}_1$ channel, and find that the tensor potential for $\Lambda_c N$isnegligiblyweakandcentralpotentialsinboth$^1S_0$and$^3S_1 - $${}^3{D}_1$ channels are almost identical with each other except at short distances. Phase shifts and scattering lengths calculated with these potentials show that the interaction of ${\mathrm{\Lambda }}_{c}N$ system is attractive and has a similar strength in ${}^1{S}_0$ and ${}^3{S}_1$ channels at low energies (i.e. the kinetic energy less than about $40$ MeV). While the attractions are not strong enough to form two-body bound states, our results lead to a possibility to form ${\mathrm{\Lambda }}_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for ${\mathrm{\Lambda }}_c$ hypernuclei from the ${\mathrm{\Lambda }}_c$-nucleon potential obtained in lattice QCD, and find that ${\mathrm{\Lambda }}_c$ hypernuclei can exist for $A\ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the ${\mathrm{\Lambda }}_c$ hypernuclei.