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