Research Article
Properties and Behaviors of Heavy Quarkonia: Insights through Fractional Model and Topological Defects
Table 1
Mass spectra of charmonium (in GeV) for two models (the classical model
and the fractional model (
, ) at
).
| State | The classical model | The fractional model | [36] | [37] | [38] | [39] | Exp. [42] | Error of the classical model | Error of the fractional model |
| 1S | 3.096 | 3.074 | 3.078 | 3.096 | 3.078 | 3.239 | 3.096 | 0 | 0.007 |
| 2S | 3.619 | 3.582 | 4.187 | 3.686 | 3.581 | 3.646 | 3.649 | 0.008 | 0.018 |
| 3S | 4.142 | 4.090 | 5.297 | 3.984 | 4.085 | 4.052 | 4.040 | 0.025 | 0.012 |
| 4S | 4.665 | 4.598 | 6.407 | 4.150 | 4.589 | 4.459 | 4.415 | 0.056 | 0.041 |
| 1P | 3.488 | 3.513 | | | | | | | | 3.619 | 3.654 | 3.415 | 3.433 | 3.415 | 3.372 | 3.525 | 0.010 | 0.003 | 3.75 | 3.796 | | | | | | | |
| 2P | 4.011 | 4.020 | | | | | | | | 4.142 | 4.163 | 4.143 | 3.910 | 3.917 | 3.779 | 3.900 | 0.005 | 0.007 | 4.273 | 4.305 | | | | | | | |
| 1D | 3.358 | 5.067 | | | | | | | | 3.75 | 4.644 | | | | | | | | 3.142 | 4.221 | 3.752 | 3.767 | 3.749 | 3.604 | 3.769 | 0.028 | 0.030 | 4.534 | 3.796 | | | | | | | | 4.927 | 3.369 | | | | | | | |
| Total error | 0.018 | 0.016 | 0.9513 | 0.11065 | 0.11152 | 0.05788 | ā | | |
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