Building diquark model from Lattice QCD

Abstract: A novel Lattice QCD (LQCD) method to determine the quark-diquark ($q$-$D$) interaction potential together with the diquark mass ($m_D$) is proposed. Similar to the HAL QCD method, $q$-$D$ potential is determined by demanding it to reproduce the $q$-$D$ equal-time Nambu-Bethe-Salpeter (NBS) wave function. To do this, it is necessary to use the masses of the quark and the diquark as inputs, which however are not straightforwardly obtained because of the color confinement of QCD. In this work, masses of quark and diquark are determined by demanding that the p-wave spectrums from the two-point correlators be reproduced by the potentials for $c$-$\bar{c}$ and $q$-$D$ sectors determined from the NBS wave functions. Numerical calculations are performed by using 2+1 flavor QCD gauge configurations with the pion mass $m_\pi\simeq 700$ MeV generated by PACS-CS collaboration. We apply our method to the $c$-$\bar c$ system and the charm-diquark system ($\Lambda_c$ baryon) to obtain the charm quark mass, diquark mass and the $c$-$D$ potential. Our preliminary analysis leads to the diquark mass $m_D \simeq 1.127$ GeV which is roughly consistent with a naive estimate based on the constituent quark picture, i.e., $m_{D} \simeq m_{\rho} \simeq 1.12$ GeV and $m_{D} \simeq 2m_N/3 \simeq 1.06$ GeV.