AI 中文总结
该研究利用凝聚态第一性原理求和规则，推导了仅依赖少数材料性质的暗物质-电子散射率上限，为相关直接探测实验的灵敏度设定了基本限制。
AI 中文摘要
多种凝聚态体系已被用作或被提议作为探测器来搜寻暗物质-电子散射。通常，散射率取决于这些体系电子性质的详细信息；但当暗物质与电子密度耦合时，暗物质-电子散射率可与电子能量损失函数相关，其积分受第一性原理求和规则约束，而这些求和规则仅依赖少数宏观靶标性质。本文利用这些第一性原理求和规则推导暗物质-电子散射率的上限，该上限仅取决于少量材料性质：等离子体频率ωₚ、靶物质密度ρ_T以及有限动量转移下的静态（纵向）介电函数ε(q,0)。ωₚ和ρ_T这类体材料性质在大量材料中仅在有限范围内变化，且在良好近似下，ε(q,0)的通用大q依赖关系可通过仅与ωₚ相关的简单标度律来理解，我们已通过解析和数值实例验证了该标度律。因此，我们推导的上限在很大程度上与材料无关，为任何探测电子密度耦合的暗物质-电子直接探测实验的灵敏度设定了基本限制。
英文摘要
A wide variety of condensed matter systems are used or proposed as detectors to search for dark matter-electron scattering. In general, the scattering rate depends on detailed knowledge of the electronic properties of these systems. However, when dark matter couples to electron density, the dark matter-electron scattering rate can be related to the electron energy loss function, whose integrals are bounded by first-principles sum rules that rely on only a few macroscopic target properties. In this paper, we use these first-principles sum rules to derive upper bounds on the dark matter-electron scattering rate depending on only a few material properties: the plasma frequency $ω_\text{p}$, the target mass density $ρ_T$, and the static (longitudinal) dielectric function at finite momentum transfer, $\varepsilon(q, 0)$. The bulk material properties $ω_\text{p}$ and $ρ_T$ vary only over a limited range across a wide variety of materials, and to a good approximation, the generic large-$q$ dependence of $\varepsilon(q, 0)$ can be understood from a simple scaling law depending only on $ω_\text{p}$ which we verify with analytic and numerical examples. Thus, our upper bounds are largely material-agnostic, and place a fundamental limit on the sensitivity of any dark matter-electron direct detection experiment probing the coupling to electron density.
Comments9 + 3 pages, 4 figures
