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arXiv 1606.06166hep-ph
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标量关联函数，希格斯衰变为夸克，以及QCD耦合的方案变化

Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling

Matthias Jamin, Ramon Miravitllas

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29 pages, 4 figures; minor modifications, version to be published in JHEP
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摘要：

本文研究了标量关联函数$Ψ(s)$的微扰QCD级数。除了与希格斯衰变为夸克有关的${\rm Im}Ψ(s)$外，另外两个物理衰变子$Ψ^{"}(s)$和$D^L(s)$也被用于QCD应用，如夸克质量测定或强子$τ$衰变。$D^L(s)$遭受大的高阶校正，并通过诉诸大- $β_0$近似，它表明，这是一个虚假的renormalon模糊在$u=1$。因此，这种关联函数在唯象分析中应该避免。此外，它被证明是有利的夸克质量因子，介绍了使标量电流重整化群不变，在重整化不变夸克质量$\hat m_q$方面。为了进一步研究微扰展开的行为，我们引入了一个QCD耦合$\hatα_s$，它的运行是明确的重整化方案无关。$\hatα_s$的方案依赖性是由一个单一的参数$C$参数化的，与QCD尺度参数$Λ$的转换。它表明，适当的选择$C$导致$Ψ^{"}(s)$和${\rm Im}Ψ(s)$的微扰系列的行为有很大的改善。

英文摘要：

In this work, the perturbative QCD series of the scalar correlation function $Ψ(s)$ is investigated. Besides ${\rm Im}Ψ(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $Ψ^{"}(s)$ and $D^L(s)$, have been employed in QCD applications like quark mass determinations or hadronic $τ$ decays. $D^L(s)$ suffers from large higher-order corrections and, by resorting to the large-$β_0$ approximation, it is shown that this is related to a spurious renormalon ambiguity at $u=1$. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass $\hat m_q$. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling $\hatα_s$, whose running is explicitly renormalisation scheme independent. The scheme dependence of $\hatα_s$ is parametrised by a single parameter $C$, being related to transformations of the QCD scale parameter $Λ$. It is demonstrated that appropriate choices of $C$ lead to a substantial improvement in the behaviour of the perturbative series for $Ψ^{"}(s)$ and ${\rm Im}Ψ(s)$.

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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