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Fine and Hyperfine Splittings of Charmonium and Bottomonium: An Improved Perturbative QCD Approach

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 نشر من قبل Stefan Recksiegel
 تاريخ النشر 2003
  مجال البحث
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We extend the formalism based on perturbative QCD that was developed in our previous work, and compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. All the corrections up to O(alpha_s^5 m) are included in the computations. We find agreement (with respect to theoretical uncertainties) with the experimental values whenever available and give predictions for not yet observed splittings.

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57 - S. Recksiegel , Y. Sumino 2002
Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the S-P splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the S-P splittings are larger than those of the boundstates themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale mu of the operator propto C_A/(m_b r^2). The agreement of the whole spectrum with the experimental data is much better than the previous predictions when mu simeq 3-4 GeV for alpha_S(M_Z)=0.1181. There seems to be a phenomenological preference for some suppression mechanism for the above operator.
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