标题： 二环重整化和星系偏差的运行 显示英文标题

标题： Two-loop renormalization and running of galaxy bias

摘要： 我们系统地将星系偏差重正化框架扩展到两环阶次。 对于密度场中五阶以下的29个确定性偏差算符的最小完整基，以及梯度展开的领先阶次，我们明确推导出一环和两环的重正化。 后者以偏差核的双重硬极限形式给出，我们发现它们仅依赖于环动量比值的一个函数。 在以复合算符重正化形式包括随机性之后，我们将该框架应用于有偏示踪物的两环功率谱，并提供一个适合数值计算的简单结果。 此外，我们推导出与从平滑密度场构造的偏差算符相关的确定性偏差系数的一环和两环重正化群方程（RGE），推广了之前的工作。 我们识别出一个具有增强紫外敏感性的偏差算符线性组合，它与RGE的一个正特征值相关。 最后，我们提出了与量子场论中使用的RGE的类比，表明如在后者中所采用的大对数重求和方法也可能在大尺度星系偏差的研究中产生有用的应用。 显示英文摘要

摘要： We systematically extend the framework of galaxy bias renormalization to two-loop order. For the minimal complete basis of 29 deterministic bias operators up to fifth order in the density field and at leading order in gradient expansion we explicitly work out one- and two-loop renormalization. The latter is provided in terms of double-hard limits of bias kernels, which we find to depend on only one function of the ratio of the loop momenta. After including stochasticity in terms of composite operator renormalization, we apply the framework to the two-loop power spectrum of biased tracers and provide a simple result suitable for numerical evaluation. In addition, we work out one- and two-loop renormalization group equations (RGE) for deterministic bias coefficients related to bias operators constructed from a smoothed density field, generalizing previous works. We identify a linear combination of bias operators with enhanced UV sensitivity, related to a positive eigenvalue of the RGE. Finally, we present an analogy with the RGE as used in quantum field theory, suggesting that a resummation of large logarithms as employed in the latter may also yield useful applications in the study of large-scale galaxy bias.