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arXiv · 1408.5590

Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order

Y. Kiyo·Y. Sumino
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Abstract

We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers $n$, $\ell$, $s$ and $j$, up to ${\cal O}(α_s^5 m)$ and ${\cal O}(α_s^5 m \log α_s)$ in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers ($π$, $ζ(3)$, $ζ(5)$) and finite sums (besides the 3-loop constant $\bar{a}_3$ of the static potential whose full analytic form is still unknown). A derivation of the formula is given.

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Y. Kiyo, Y. Sumino. 2017-03-31. Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order. https://doi.org/10.1016/j.nuclphysb.2014.10.010

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