Building Diquark Model from Lattice QCD

• Published in: Few-body systems Vol. 62; no. 3
• Main Authors: Watanabe, Kai, Ishii, Noriyoshi
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.09.2021; Springer Nature B.V
• Subjects: Advances on the Few-Body Problem in Physics – Selected and Refereed papers from the 8th Asia-Pacific Conference; Atomic; Charm (particle physics); Correlators; Flavor (particle physics); Hadrons; Heavy Ions; Molecular; Nuclear Physics; Optical and Plasma Physics; P waves; Particle and Nuclear Physics; Physics; Physics and Astronomy; Pions; Quantum chromodynamics; Quantum confinement; Quarks; Wave functions; Lattice QCD; Hadron structure; Hadron interactions
• ISSN: 0177-7963; 1432-5411
• DOI: 10.1007/s00601-021-01627-y

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 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 π ≃ 700 MeV generated by PACS-CS collaboration. We apply our method to the c – c ¯ system and the charm-diquark system ( Λ 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 ≃ 1.127  GeV which is roughly consistent with a naive estimate based on the constituent quark picture, i.e., m D ≃ m ρ ≃ 1.12  GeV and m D ≃ 2 m N / 3 ≃ 1.06  GeV.