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 $2m_N/3$.

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

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• Nuclear Force from Lattice QCD
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Cited by in corpus (1)

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