Quark-diquark potential and diquark mass from Lattice QCD

Abstract

We propose a new application of lattice QCD to calculate the quark-diquark potential, diquark mass and quark mass required for the diquark model. As a concrete example, we consider the ${\Lambda }_c$ baryon and treat it as a charm-diquark($c$-[$ud$]) two-body bound state. We extend the HAL QCD method to calculate the charm-diquark potential which reproduces the equal-time Nambu-Bethe-Salpeter wave function of the S-wave state (${\Lambda }_c({\frac{1}{2}}^{+})$). The diquark mass is determined so as to reproduce the difference between the S-wave and the spin-orbit averaged P-wave energies, i.e. the difference between the ${\Lambda }_c({\frac{1}{2}}^{+})$ level and the average of the ${\Lambda }_c({\frac{1}{2}}^{-})$ and the ${\Lambda }_c({\frac{3}{2}}^{-})$ levels. Numerical calculations are performed on a $32^3\times 64$ lattice with lattice spacing of $a\simeq 0.0907$ fm and the pion mass of $m_{\pi }\simeq 700$ MeV. Our charm-diquark potential is given by the Coulomb+linear (Cornell) potential where the long range behavior is consistent with the charm-anticharm potential while the Coulomb attraction is considerably smaller. This weakening of the attraction may be attributed to the diquark size effect. The obtained diquark mass is $m_D=1.273(44)$ GeV. Our diquark mass lies slightly above the conventional estimates, namely the $\rho$ meson mass and twice the constituent quark mass $2m_N/3$.

arXiv comment14 pages, 15 figures. Revised on 2022 March 4th. Minor changes were made to align with the version published in PRD.[Augast 14th]

References in corpus (38)

• QCD forces and heavy quark bound states
• Exotica
• Nuclear Force from Lattice QCD
• 2+1 Flavor Lattice QCD toward the Physical Point
• Observation of String Breaking in QCD
• The New Pentaquarks in the Diquark Model
• Three-Quark Potential in SU(3) Lattice QCD
• Baryon spectrum with $N_f=2+1+1$ twisted mass fermions
• Nonperturbative determination of the QCD potential at O(1/m)
• An interacting quark-diquark model of baryons
• Charmed baryons at the physical point in 2+1 flavor lattice QCD
• Octet and Decuplet Baryons in a Covariant and Confining Diquark-Quark Model
• Evidence for diquarks in lattice QCD
• Relativistic Heavy Quarks on the Lattice
• The Simple Spectrum of $c\bar{c}c\bar{c}$ States in the Dynamical Diquark Model
• Diquark Masses from Lattice QCD
• I=2 Pion Scattering Length from Two-Pion Wave Functions
• Building the International Lattice Data Grid
• Lattice QCD and baryon-baryon interactions: HAL QCD method
• Nonperturbative $O(a)$ improvement of the Wilson quark action with the RG-improved gauge action using the Schrödinger functional method
• Interquark potential with finite quark mass from lattice QCD
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Spin-3/2 Nucleon and Delta Baryons in Lattice QCD
• Charmed baryon spectrum from lattice QCD near the physical point
• Understanding the nucleon as a Borromean bound-state
• Structure of the nucleon's low-lying excitations
• Heavy pentaquark spectroscopy in the diquark model
• Effective string theory constraints on the long distance behavior of the subleading potentials
• Diquarks as Inspiration and as Objects
• Three-quark potential and Abelian dominance of confinement in SU(3) QCD
• Potential description of charmonium and charmed-strange mesons from lattice QCD
• Diquark mass differences from unquenched lattice QCD
• I=2 Two-Pion Wave Function and Scattering Phase Shift
• Quark-anti-quark potentials from Nambu-Bethe-Salpeter amplitudes on lattice
• Bethe-Salpeter wave functions of ${\eta }_c(2S)$ and $\psi (2S)$ states from full lattice QCD
• Quark confinement potential examined by excitation energy of the Lambda_c and Lambda_b baryons in a quark-diquark model
• Excitation energy spectra of the Lambda_c and Lambda_b baryons in a finite-size diquark model
• Spin-3/2 Baryons in Lattice QCD

Cited by in corpus (1)

• Strong decays of singly heavy baryons from a chiral effective theory of diquarks