“上帝的手指”能否被重求和？
Can Fingers of God be Resummed?
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究所）
- Department of Physics, Columbia University（哥伦比亚大学物理系）
- NASA Hubble Fellowship Program（NASA哈勃奖学金计划）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文探讨红移巡天中“上帝的手指”效应能否被严格重求和，证明常见阻尼模型仅为平均场极限，环境修正破坏其形式，需扩展算符基并引入依赖波数的系数，结论为可能但代价高昂。
AI中文摘要：
“上帝的手指”（FoGs），即由于星系小尺度维里运动引起的多普勒频移，是红移巡天中星系成团性解析模型面临的最重大挑战之一。在有效场论方法中，这些频移的特征尺度引入了一个新的、较大的长度尺度，限制了理论的适用范围。这促使文献中出现了许多关于FoGs的现象学模型，其中其效应被近似为视线波数$\lambda=k\mu$的单一阻尼函数，实际上是通过小尺度速度的单点收缩对$\lambda$的幂次进行重求和。本工作的目标是研究这种重求和能否被严格构建。我们表明，常见的阻尼模型可以理解为FoG速度的单粒子特征函数（SPCF）的平均场极限，但SPCF的环境依赖性会产生同样大的修正，从而破坏简单的阻尼形式。我们发展了SPCF的长波理论，表明它允许在各项异性偏置算符中进行展开，这些算符与为选择效应推导的算符密切相关，但具有满足选择规则的$\lambda$依赖系数。我们使用类DESI星系的光晕模型估计这些系数，表明它们在星系的2点和3点相关函数层面做出了显著贡献。回答标题中的问题：可能可以，但代价是显著扩展算符基并将自由系数提升为自由函数。
英文摘要：
Fingers of God (FoGs), Doppler shifts due to the small-scale virial motions of galaxies, are one of the most significant challenges for analytic models of galaxy clustering in redshift surveys. In the effective field theory approach, the characteristic scale of these shifts introduces a new, large length scale, limiting the reach of the theory. This has motivated many phenomenological models of FoGs in the literature where their effect is approximated by a single damping function of the line-of-sight wavenumber $λ=kμ$, effectively resumming powers of $λ$ due to single-point contractions of small-scale velocities. The goal of this work is to investigate whether such a resummation can be rigorously constructed. We show that common damping models can be understood as the mean-field limit of the single-particle characteristic function (SPCF) of FoG velocities, but that the environmental dependence of the SPCF generates equally large corrections that break the simple damping form. We develop the long-wavelength theory of the SPCF, showing that it admits an expansion in anisotropic bias operators closely related to those derived for selection effects, but with $λ$-dependent coefficients satisfying selection rules. We estimate these coefficients using the halo model for DESI-like galaxies, showing that they make significant contributions at the level of the 2- and 3-point functions of galaxies. To answer the titular question: potentially, but at the cost of significantly expanding the operator basis and promoting free coefficients to free functions.
