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arXiv 1408.5590hep-ph
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次次次领头阶级重夸克偶素能级的全公式

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

Y. Kiyo, Y. Sumino

摘要:

在微扰QCD中,我们导出了重夸克偶素态能级的完整公式,量子数为$n$,$\ell$,$s$和$j$,直到${\cal O}(α_s^5 m)$和${\cal O}(α_s^5 m \log α_s)$。给出了QCD Bethe对数的单参数积分形式。公式的其余部分由有理数、超越数($π$、$ζ(3)$、$ζ(5)$)和有限和(除了静电势的3圈常数$\bar{a}_3$,其完整的解析形式仍然未知)的组合给出。给出了公式的推导过程。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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