Diquark mass and quark-diquark potential by lattice QCD using an extended HAL QCD method with a static quark

We will calculate the diquark mass together with the quark-diquark potential. We apply an extended HAL QCD potential method to a baryonic system made up from a static quark and a diquark. Numerical calculations are performed by employing 2+1 flavor QCD gaugeconfigurations generated by CP-PACS and JLQCD Collaborations on a $16^{3} \times 32$ lattice with $a^{-1} \approx 1.6$ GeV. To improve the statistical noise in the propagators of the static quark, the HYP smearing is employed on the gauge links. Two-point correlators of quark-diquark baryonic system are then computed to obtain their ground-state energies where various types of diquarks are considered (eg: scalar diquark, axial-vector diquark etc). We apply an extended HAL QCD method on a baryonic system made up from a scalar diquark and a static quark to study the scalar diquark mass and the quark-diquark potential. In order to determine the diquark mass self-consistently in this HALQCD method, we demand that the baryonic spectrum in the p-wave sector obtained from the two-point correlators should be reproduced by the potential obtained from the baryonic system in the s-wave sector. We obtain the scalar diquark mass of roughly $(2/3) m_{N}$ , i.e., twice the na\"ive estimates of a constituent quark mass together with the quark-diquark potential of Cornell type (Coulomb + linear).