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arXiv 1809.09124hep-phhep-latnucl-th
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对数精度为次领先的P波重夸克偶素谱

P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

Clara Peset, Antonio Pineda, Jorge Segovia

摘要:

我们计算了重夸克偶素质量的$l\not= 0$(角动量)状态,否则任意的量子数,下一次到下一次到领先的对数(N $^3$ LL)的准确性。这构成了在重夸克偶素中的第一个可观测到的结果,其中两个对超软标度敏感的弱耦合膨胀是已知的,并对超软标度进行了重新确认。我们还首次得到了这些态的精细和超精细能量分裂的简化N $^3$ LL表达式,这些表达式对超软尺度不敏感,但仍需要对(硬)谱进行重新计算。我们对质量相等和质量不等的情况进行分析。我们还研究了另一种计算方案,对待静态电位。然后,我们进行了全面的唯象分析:我们将这些结果应用到$n=2$,$l=1$ bottomonium,$B_c$和charmonium系统,并研究其收敛性。

英文摘要:

We compute the heavy quarkonium mass of $l\not= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. This constitutes the first observable in heavy quarkonium for which two orders of the weak-coupling expansion sensitive to the ultrasoft scale are known and the resummation of ultrasoft logarithms is made. We also obtain, for the first time, resummed N$^3$LL expressions for the different fine and hyperfine energy splittings of these states, which are not sensitive to the ultrasoft scale but still require resummation of (hard) logarithms. We do this analysis for the equal and non-equal mass cases. We also study an alternative computational scheme that treats the static potential exactly. We then perform a comprehensive phenomenological analysis: we apply these results to the $n=2$, $l=1$ bottomonium, $B_c$ and charmonium systems and study their convergence.

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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