论文标题
对$τ$ hadronic Spectral Moments II：Renormalon Norm和$α_S$确定的$τ$ HADRONE SPESTRAN MOMENTS的轮廓改良和固定顺序方法
Reconciling the Contour-Improved and Fixed-Order Approaches for $τ$ Hadronic Spectral Moments II: Renormalon Norm and Application in $α_s$ Determinations
论文作者
论文摘要
In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $τ$ hadronic spectral function moments, which had affected the precision of $α_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element.另外，可以改善光谱功能矩的扰动收敛性，可以改善具有相当大的GC校正。 RF GC方案取决于IR分解量表$ r $和GC Renormalon的归一化$ n_g $。在目前的工作中，我们使用三种不同的方法来确定$ n_g $，从而产生了不确定性$ 40 \％$的结果。遵循$ {\ cal o}（α_s^5）$的两个最新最新的强耦合测定分析，我们表明，使用无肾上腺龙的GC方案成功地将基于$α_s（{m__τ2}）的结果核算基于CIPT和FOPT。由于$ r $的变化和$ n_g $的不确定性引起的不确定性仅导致最终不确定性$α_s（m_τ^2）$的小幅增加或中等增加，并且主要影响CIPT扩展方法。在RF GC方案中获得的FOPT和CIPT结果可以始终平均。因此，RF GC方案构成了一种强大的新成分，用于将来分析$τ$ HADRONIC光谱功能矩。
In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $τ$ hadronic spectral function moments, which had affected the precision of $α_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element. In addition, the perturbative convergence of spectral function moments with a sizeable GC correction can be improved. The RF GC scheme depends on an IR factorization scale $R$ and the normalization $N_g$ of the GC renormalon. In the present work, we use three different methods to determine $N_g$, yielding a result with an uncertainty of $40\%$. Following two recent state-of-the-art strong coupling determination analyses at ${\cal O}(α_s^5)$, we show that using the renormalon-free GC scheme successfully reconciles the results for $α_s({m_τ^2})$ based on CIPT and FOPT. The uncertainties due to variations of $R$ and the uncertainty of $N_g$ only lead to a small or moderate increase of the final uncertainty of $α_s(m_τ^2)$, and affect mainly the CIPT expansion method. The FOPT and CIPT results obtained in the RF GC scheme may be consistently averaged. The RF GC scheme thus constitutes a powerful new ingredient for future analyses of $τ$ hadronic spectral function moments.
