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Nonrelativistic Heavy Quarkonium Model Descended from a Quasi-Particle Approach

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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

  1. For example, cf. Text book by Ynduráin [1].

  2. To control the infrared divergence of \(\hat{v}(|k|)\), the limit \(\mu \rightarrow 0\) was taken after the integration was performed.

  3. 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 \(x=r\).

  4. 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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Authors and Affiliations

  1. Hokkaido University of Education, Sapporo, 002-8502, Japan

    M. Sakai & M. Hirano

  2. Hokkaido Hadron Study Association, Sapporo, 005-0861, Japan

    M. Sakai, M. Hirano, K. Katō & Y. Matsuda

  3. Nuclear Reaction Data Centre, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    K. Katō

Authors
  1. M. Sakai
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  2. M. Hirano
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  3. K. Katō
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  4. Y. Matsuda
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Correspondence to K. Katō.

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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