论文标题
$γ+η_c$的比例固定预测在扰动QCD中的nnlo中的电子峰值碰撞中产生
Scale-Fixed Predictions for $γ+ η_c$ production in electron-positron collisions at NNLO in perturbative QCD
论文作者
论文摘要
在本文中，我们提出了$η_{C} +γ$在电子位置对撞机上产生的QCD预测，直到近代到领先顺序（NNLO）精确度，而无需重新归一化量表。使用传统的比例设定方法使用$ E^{+}+e^{ - } \toγ+η_{C} $的NNLO总横截面具有较大的重归于量表级别的歧义，通常通过选择重新归一化量表作为$ E^+e^+e^+e^ - $中心碰撞的能量$ \ s sqrt。最大相结合原理（PMC）提供了一种系统的方法来消除这种重新归一化量表的歧义，通过将非符号$β$贡献求和到QCD耦合$α_s（q^2）$。然后，重新归一化组方程为该过程设置$α_s$的值。 PMC重新归一化量表反映了基本过程的虚拟性，而由此产生的预测满足了重新归一化组不变性的所有要求，包括重新归一化方案不变性。应用PMC后，我们获得了一个比例独立预测，$σ| _ {\ rm nnlo，pmc} \ simeq 41.18 $ fb for $ \ sqrt {s} $ = 10.6 gev。由此产生的PQCD系列与保形理论相匹配，因此没有发散的肾上腺素贡献。有助于这一过程的大$ K $因子增强了未算出的NNLO和高阶条款的重要性。使用PMC比例比例独立的共振序列和$ \ rm pad \ Acute {e} $近似方法，我们预测$σ| _ {\ rm nnnlo，pmc+pade} \ simeq 21.36 $ fb，这与最近的Belle Muesurement $ fum $σ^^{\ rm fb是一致的obs} $ = $ 16.58^{+10.51} _ { - 9.93} $ fb at $ \ sqrt {s} \ simeq 10.6 $ gev。该程序还提供了NNNLO贡献的第一个估计。
In the paper, we present QCD predictions for $η_{c} + γ$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\toγ+η_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling $α_s(Q^2)$. The renormalization group equation then sets the value of $α_s$ for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a scale-and-scheme independent prediction, $σ|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large $K$ factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the $\rm Pad\acute{e}$ approximation approach, we predict $σ|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $σ^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution.
