Quark-diquark potential and diquark mass from lattice QCD

We propose a new application of lattice QCD to calculate the quark-diquark potential, diquark mass, and quark mass required for model. As concrete example, we consider ${\mathrm{\ensuremath{\Lambda}}}_{c}$ baryon treat it as charm-diquark ($c$-[$ud$]) two-body bound state. extend HAL method which reproduces equal-time Nambu-Bethe-Salpeter wave function S-wave state [${\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{1}{2}}^{+})$]. The is determined so reproduce difference between spin-orbit averaged P-wave energies, i.e., ${\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{1}{2}}^{+})$ level average ${\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{1}{2}}^{\ensuremath{-}})$ ${\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{3}{2}}^{\ensuremath{-}})$ levels. Numerical calculations are performed on ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ with spacing $a\ensuremath{\simeq}0.0907\text{ }\text{ }\mathrm{fm}$ pion ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}700\text{ }\mathrm{MeV}$. Our potential given by $\mathrm{Coulomb}+\mathrm{linear}$ (Cornell) where long range behavior consistent charm-anticharm while Coulomb attraction considerably smaller. This weakening may be attributed size effect. obtained ${m}_{D}=1.273(44)\text{ }\mathrm{GeV}$. lies slightly above conventional estimates, namely $\ensuremath{\rho}$ meson twice constituent $2{m}_{N}/3$.