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

TL;DR

This paper addresses the challenge of determining diquark properties within QCD by employing an extended HAL QCD approach with a static quark to form a baryon-like system. By extracting equal-time NBS wavefunctions for a static-quark–diquark setup and enforcing consistency between the P-wave and S-wave sectors, the authors determine the scalar diquark mass $m_D$ and reconstruct the quark–diquark potential $V_0(r)$, avoiding ambiguities associated with finite-mass charm quarks. They find $m_D \simeq 1.241$ GeV and a Cornell-like potential $V_0(r) = -A/r + Br + v_0$ with $A=0.121(4)$ GeV·fm, $\sqrt{B}=510(5)$ MeV, and $v_0=0.141(15)$ GeV, with short-distance behavior affected by HYP smearing. The work demonstrates explicit decomposition of baryon mass into the diquark mass and interaction energy, providing a pathway to extrapolations to physical quark masses and extensions to axial-vector diquarks.

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 naïve estimates of a constituent quark mass together with the quark-diquark potential of Cornell type (Coulomb + linear).

Figures (4)

• Figure 1: Effective mass differences $\Delta m_{C\Gamma}$ for baryonic states corresponding to various diquark channels, computed from wall-sourced two-point correlators.
• Figure 2: Convergence behavior of four-point correlators using three types of sources. SRC01 and SRC03 denote exponentially smeared sources with $f(r) = \exp(-r)$ and $\exp(-r/3)$, respectively (in lattice units). SRC08 denotes the wall source. Convergence rate: SRC01 > SRC03 > SRC08.
• Figure 3: Prepotentials for $t/a = 2, 4, \dots, 14$ using SRC01.
• Figure 4: The quark–diquark potential.