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

TL;DR

This paper calculates the scalar diquark mass and quark-diquark potential using an extended HAL QCD method with lattice QCD, providing insights into baryonic systems with static quarks and diquarks.

Contribution

It introduces an extended HAL QCD approach to determine diquark masses and potentials self-consistently in lattice QCD with static quarks.

Findings

Scalar diquark mass is approximately two-thirds of the nucleon mass.

The quark-diquark potential has a Cornell type form (Coulomb + linear).

The method reproduces baryonic spectra in the p-wave sector.

Abstract

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).