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

Abstract

The interaction between ${\Lambda }_c$ and a nucleon ($N$) is investigated by employing the HAL QCD method in the (2+1)-flavor lattice QCD on a $(2.9\mathrm{fm}{)}^3$ 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-$${}^3{D}_1$ channel, and find that the tensor potential for ${\Lambda }_{c}N$ is negligibly weak and central potentials in both ${}^1{S}_0$ and ${}^3{S}_1-$${}^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 ${\Lambda }_{c}N$ 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 ${\Lambda }_c$ hypernuclei for sufficiently large atomic numbers ($A$). To demonstrate this, we derive a single-folding potential for ${\Lambda }_c$ hypernuclei from the ${\Lambda }_c$-nucleon potential obtained in lattice QCD, and find that ${\Lambda }_c$ hypernuclei can exist for $A\ge 12$ with the binding energies of a few MeV. We also estimate the Coulomb effect for the ${\Lambda }_c$ hypernuclei.

Comments: 27 pages, 10 figures, 4 tables