Building diquark model from Lattice QCD

TL;DR

This paper introduces a new Lattice QCD method to determine the quark-diquark interaction potential and diquark mass by reproducing NBS wave functions, providing insights into diquark structure within QCD.

Contribution

A novel Lattice QCD approach to extract the quark-diquark potential and diquark mass from NBS wave functions, applicable to charm systems and baryons.

Findings

Diquark mass estimated at approximately 1.127 GeV.

Method successfully reproduces p-wave spectra for charm systems.

Results consistent with naive constituent quark model estimates.

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.