AI 中文总结
本研究针对半导体轻暗物质-电子散射介电形式体系中横向响应被忽略的问题，在均匀电子气无规相近似下推导并定量评估了横向介电函数，验证了硅体等离激元区纵向近似的合理性，给出了纵向计算的误差评估与需纳入横向修正的运动学区间。
AI 中文摘要
迄今为止，半导体中轻暗物质-电子散射的介电形式体系仅采用了纵向介电函数$ε_L$，而横向响应$ε_T$则基于定性理由被普遍忽略。目前仍缺乏针对该场景下$ε_T$的完整推导与定量评估。我们在均匀电子气的无规相近似（random phase approximation）框架下完成了这一推导。针对硅材料，我们发现在体等离激元区域，横向能量损失函数比纵向能量损失函数低4–6个数量级，这为传统的纵向近似提供了首个严格的理论依据。显著的横向修正出现在沉积能量$ω\lesssim1\\,\mathrm{eV}$的区间，该能量低于硅探测器中可靠产生一个电子-空穴对所需的能量。我们的结果为现有的纵向计算提供了定量的误差评估，并明确了在相对论性暗物质的诠释中需要纳入横向修正的运动学区域。
英文摘要
The dielectric formalism for light dark matter--electron scattering in semiconductors has, to date, employed only the longitudinal dielectric function $ε_L$, with the transverse response $ε_T$ universally neglected on qualitative grounds. A complete derivation and quantitative evaluation of $ε_T$ in this context has been lacking. We provide this derivation within the random phase approximation for a homogeneous electron gas. For silicon, we find that the transverse energy loss function is $4--6$ orders of magnitude below the longitudinal one in the bulk plasmon regime, providing the first rigorous justification for the conventional longitudinal approximation. The sizable transverse corrections appear for deposited energies $ω\lesssim1\,\mathrm{eV}$, which lies below the energy required to reliably produce one electron-hole pair in silicon detectors. Our results provide a quantitative error assessment for existing longitudinal calculations and identify kinematic regimes where transverse corrections ought to be included for relativistic dark-matter interpretations.
Comments6 pages, 2 figures
