Abstract
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.
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Notes
For example, cf. Text book by Ynduráin [1].
To control the infrared divergence of \(\hat{v}(|k|)\), the limit \(\mu \rightarrow 0\) was taken after the integration was performed.
The integral term in Eq. (3.10) has a well-defined value in the singular integral sense, despite the logarithmic divergence on the straight line \(x=r\).
As another possible example of a physical quantity related to the wave function of the heavy quarkonium, a picture for the open flavor decays has been proposed [19].
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Sakai, M., Hirano, M., Katō, K. et al. Nonrelativistic Heavy Quarkonium Model Descended from a Quasi-Particle Approach. Few-Body Syst 64, 2 (2023). https://doi.org/10.1007/s00601-022-01782-w
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DOI: https://doi.org/10.1007/s00601-022-01782-w