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.

提出了一种新的格子 QCD (LQCD) 方法来确定夸克-双夸克 ( q – D ) 相互作用势以及双夸克质量 ( \(m_D\) )。与 HAL QCD 方法类似，q - D电位是通过要求它重现q - D等时 Nambu-Bethe-Salpeter (NBS) 波函数来确定的。为此，必须使用夸克和迪夸克的质量作为输入，但由于 QCD 的颜色限制，无法直接获得这些质量。在这项工作中，夸克和迪夸克的质量是通过要求来自两点相关器的 p 波谱由\(c{\bar{c}}\)和q - d从NBS确定扇区波函数。数值计算是通过使用 2+1 风味 QCD 规配置和PACS-CS 协作生成的 pion 质量\(m_\pi \simeq 700\) MeV 进行的。我们将我们的方法应用于c – \({\bar{c}}\)系统和粲-迪夸克系统（\(\Lambda _c\)重子）以获得粲夸克质量、迪夸克质量和c – D潜在的。我们的初步分析导致迪夸克质量\(m_D \simeq 1.127\)  GeV 与基于组成夸克图片的朴素估计大致一致，即\(m_{D} \simeq m_{\rho } \simeq 1.12 \) GeV 和\(m_{D} \simeq 2m_N/3 \simeq 1.06\)  GeV。