Nonrelativistic Heavy Quarkonium Model Descended from a Quasi-Particle Approach

• Published in: Few-body systems Vol. 64; no. 1; p. 2
• Main Authors: Sakai, M., Hirano, M., Katō, K., Matsuda, Y.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01-03-2023; Springer Nature B.V
• Subjects: Approximation; Atomic; Constituents; Elementary excitations; Hadrons; Heavy Ions; Mathematical models; Molecular; Nuclear Physics; Optical and Plasma Physics; Parameters; Particle and Nuclear Physics; Physics; Physics and Astronomy; Quark models; Quarks; S waves
• ISSN: 0177-7963; 1432-5411
• DOI: 10.1007/s00601-022-01782-w

A Schrödinger-type equation for a heavy quarkonium in terms of the dynamical quark mass is obtained in a quasi-particle approach by Llanes-Estrada and Cotanch. To observe the relationship between the obtained equation and the constituent quark (potential) model equation, we treat the dynamical quark mass by a constant parameter
M
and expand the equation in 1/
M
up to order (1/
M
). The equation reduces to that of the traditional nonrelativistic constituent quark model when a nonlocal interaction is neglected. We investigate the nonrelativistic model where the dynamical quark mass
M
in the Schrödinger-type equation is treated as a free parameter and call it the quasi-quark (QQ) model. To elucidate the role of the nonlocal interaction and to observe the reliability of the QQ model, we studied the charmonium
S
-wave states.