论文标题
集成频谱功能矩和$α_s$提取的雷诺马隆
Renormalons in integrated spectral function moments and $α_s$ extractions
论文作者
论文摘要
$α_s$从$τ\ to {\ rm（hadrons）}+ν_τ$的精确提取，从$ E^+e^ - \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ rm（hadrons）} $低于魅力阈值依赖有限的能量总规则（FESR）（FESR），在该范围内通过集成的光谱函数符号给出。在这里，我们研究了在多项式矩的Borel变换中出现的肾小球，以$β_0$限制和完整的QCD中出现。在总体$β_0$中，我们在文献中经常使用的时刻的瞬间扰动行为之间建立了直接联系。领先的IR奇异性特别突出，是扰动系列不稳定的时刻的命运，而具有良好扰动行为的人则受益于部分肾上腺素奇异性。结论可以通过方便的方案转换到$ C $ -Scheme以及使用改良的Borel变换，从而将结论扩展到QCD，从而使结果特别简单；领先的红外奇异性变成了一个简单的极点，就像$β_0$一样。最后，在表现出良好的扰动行为的时刻，我们讨论了基于重态度方案（或刻度）变化的优化截断。我们的结果可以更深入地了解集成光谱函数力矩的扰动行为，并为低$ q^2 $ $ a_s $确定提供理论支持。
Precise extractions of $α_s$ from $τ\to {\rm (hadrons)}+ν_τ$ and from $e^+e^-\to {\rm (hadrons)}$ below the charm threshold rely on finite energy sum rules (FESRs) where the experimental side is given by integrated spectral function moments. Here we study the renormalons that appear in the Borel transform of polynomial moments in the large-$β_0$ limit and in full QCD. In large-$β_0$, we establish a direct connection between the renormalons and the perturbative behaviour of moments often employed in the literature. The leading IR singularity is particularly prominent and is behind the fate of moments whose perturbative series are unstable, while those with good perturbative behaviour benefit from partial cancellations of renormalon singularities. The conclusions can be extended to QCD through a convenient scheme transformation to the $C$-scheme together with the use of a modified Borel transform which make the results particularly simple; the leading IR singularity becomes a simple pole, as in large-$β_0$. Finally, for the moments that display good perturbative behaviour, we discuss an optimized truncation based on renormalisation scheme (or scale) variation. Our results allow for a deeper understanding of the perturbative behaviour of integrated spectral function moments and provide theoretical support for low-$Q^2$ $α_s$ determinations.
