Improved perturbative QCD approach to the bottomonium spectrum

2002/07/31 by S. Recksiegel, Stefan Recksiegel, Y. Sumino · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1103/physrevd.67.014004

published as Phys.Rev. D67 (2003) 014004 · 26 pages, 16 figures. Minor changes, to be published in PRD

arxiv created 2002/11/22 · openalex publication_date 2003/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the nonrelativistic bound state 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(\ensuremathα_S⁵m_b) and O(\ensuremathα_S⁴m_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 bound states themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale \ensuremathμ of the operator \ensuremath∝C_A/(m_br²). The agreement of the whole spectrum with the experimental data is much better than the previous predictions when \ensuremathμ\ensuremath≃3--4GeV for \ensuremathα_S(M_Z)=0.1181. There seems to be a phenomenological preference for some suppression mechanism for the above operator.

Citations

• Bdecays in the upsilon expansion
• Charmonium: Comparison with experiment

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