We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the "rapidity identity operators", that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $\mathcal{N}$=4 super-Yang-Mills. These logarithms can also be extracted to $\mathcal{O}(\alpha_s^3)$ from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawson's integral, with an argument related to the cusp anomalous dimension. We call this functional form "Dawson's Sudakov". Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the $p_T$ spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.

中文翻译：

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快速对数的细分幂求和：$$ \mathcal{N} $$ = 4 SYM 中的能量-能量相关器

我们推导出并求解重整化群方程，这些方程允许对次领先的功率快速对数求和。我们的方程涉及将算子混合到一类新的算子中，我们将其称为“快速恒等算子”，在涉及快速性和虚拟性尺度的问题中，它通常会以次领先的能力出现。为了说明我们的形式主义，我们分析求解这些方程以恢复出现在 $\mathcal{N}$=4 super 中能量-能量相关器 (EEC) 的背靠背（双光锥）极限中的功率抑制对数-杨-米尔斯。这些对数也可以从最近的微扰计算中提取到 $\mathcal{O}(\alpha_s^3)$，我们发现这个顺序完全一致。而不是标准的苏达科夫指数，我们对次领先幂对数的推算结果用 Dawson 积分表示，参数与尖点异常维数有关。我们称这种函数形式为“Dawson's Sudakov”。我们的形式主义广泛适用于在其他更与现象学相关的可观测量中对次领先的功率快速对数求和，例如 QCD 中的 EEC，强子对撞机中彩色单线态玻色子产生的 $p_T$ 光谱，以及功率抑制对数的求和雷格限制。