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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.02524 |
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| _version_ | 1866915648468156416 |
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| author | Song, Lin-Qing Zhou, Hai-Qing |
| author_facet | Song, Lin-Qing Zhou, Hai-Qing |
| contents | This study presents a systematic estimation of the relativistic correction to the binding energies of two-body hadronic molecular states by comparing the numerical solutions of the three-dimensional (3D) Schr{ö}dinger, 3D Salpeter, and fully relativistic four-dimensional (4D) Bethe-Salpeter (BS) equations derived from the same underlying interaction. The numerical results reveal a counter-intuitive property: for hadronic molecular states whose binding energies are in the MeV range, the relativistic correction is unexpectedly large. This finding contradicts the conventional expectation that a heavier exchanged mass in the interaction implies suppressed relativistic effects. Specifically, we first benchmark the results using the Wick-Cutkosky model with a one-boson-exchange (OBE) interaction of mass $m_{ex}$, and then extend the analysis to the physical $D\bar{D}$ system. We find within the $1\sim 50$ MeV binding energy region, the relativistic correction is substantial, amounting to $-90\% \sim -70\%$ of the non-relativistic result. Such a significant correction strongly suggests that analyses based solely on the 3D Schr{ö}dinger or 3D Salpeter equations for hadronic molecular states should be treated with caution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relativistic correction to the binding energies of two-body hadronic molecular states Song, Lin-Qing Zhou, Hai-Qing High Energy Physics - Phenomenology High Energy Physics - Experiment This study presents a systematic estimation of the relativistic correction to the binding energies of two-body hadronic molecular states by comparing the numerical solutions of the three-dimensional (3D) Schr{ö}dinger, 3D Salpeter, and fully relativistic four-dimensional (4D) Bethe-Salpeter (BS) equations derived from the same underlying interaction. The numerical results reveal a counter-intuitive property: for hadronic molecular states whose binding energies are in the MeV range, the relativistic correction is unexpectedly large. This finding contradicts the conventional expectation that a heavier exchanged mass in the interaction implies suppressed relativistic effects. Specifically, we first benchmark the results using the Wick-Cutkosky model with a one-boson-exchange (OBE) interaction of mass $m_{ex}$, and then extend the analysis to the physical $D\bar{D}$ system. We find within the $1\sim 50$ MeV binding energy region, the relativistic correction is substantial, amounting to $-90\% \sim -70\%$ of the non-relativistic result. Such a significant correction strongly suggests that analyses based solely on the 3D Schr{ö}dinger or 3D Salpeter equations for hadronic molecular states should be treated with caution. |
| title | Relativistic correction to the binding energies of two-body hadronic molecular states |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2512.02524 |