从宇宙的结构形成来约束FIMP：从$m_{\mathrm{WDM}}$的解析映射
Constraining FIMP from the structure formation of the Universe: analytic mapping from $m_{\mathrm{WDM}}$
摘要：
相对于弱相互作用大质量粒子，弱相互作用大质量粒子是一种有趣的暗物质候选者。光（keV尺度）FIMP DM特别令人感兴趣：它的辐射衰减在X射线光谱中留下了线信号;它是温暖的暗物质（WDM），并改变了宇宙的银河系尺度结构形成与WIMP DM。一旦报告了可能的X射线线（例如，$3.5 \,\mathrm{keV}$线和$7 \,\mathrm{keV}$ FIMPDM推断），必须检查该FIMPDM是否与结构形成相容。这里有一个问题：对WDM的结构形成约束通常以所谓的热WDM质量$m_{\mathrm{WDM}}$来报告，其不能直接应用于FIMP参数。在本文中，我们介绍了一个基准的FIMP模型，代表了广泛的一类FIMP模型。该基准的一大优点是，我们可以推导出由冷冻过程产生的FIMPs的非热相空间分布的解析公式。通过进一步导出某个“温暖度”量，我们可以解析地将$m_{\mathrm{WDM}}$映射到FIMP参数。我们的分析图表明，$7 \,\mathrm{keV}$ FIMP DM，没有熵产生或退化的光谱，是在紧张局势与最新的莱曼- $α$森林数据。我们的分析地图将是非常有用的观测约束和报告的X射线线的未来更新。它也是非常容易将我们的解析公式纳入玻尔兹曼求解器，使线性物质功率谱是容易获得的。我们的基准模型将促进FIMP搜索和粒子物理模型的建立。
英文摘要：
A feebly interacting massive particle (FIMP), contrasting with a weakly interacting massive particle (WIMP), is an intriguing dark matter (DM) candidate. Light (keV-scale) FIMP DM is of particular interest: its radiative decay leaves a line signal in x-ray spectra; and it is warm dark matter (WDM) and alters the galactic-scale structure formation of the Universe from that with WIMP DM. Once a possible x-ray line is reported (e.g., $3.5 \,\mathrm{keV}$ line and $7 \,\mathrm{keV}$ FIMP DM is inferred), one has to check whether or not this FIMP DM is compatible with the structure formation. Here is an issue: the structure formation constraint on WDM is often reported in terms of the so-called thermal WDM mass $m_{\mathrm{WDM}}$, which cannot be directly applied to FIMP parameters. In this paper, we introduce a benchmark FIMP model that represents well a broad class of FIMP models. A big advantage of this benchmark is that we can derive the analytic formula of the non-thermal phase space distribution of FIMPs produced from freeze-in processes. By further deriving a certain "warmness" quantity, we can analytically map $m_{\mathrm{WDM}}$ to FIMP parameters. Our analytic map indicates that $7 \,\mathrm{keV}$ FIMP DM, without entropy production or a degenerate spectrum, is in tension with the latest Lyman-$α$ forest data. Our analytic map will be very useful for future updates of observational constraints and reports of x-ray lines. It is also very easy to incorporate our analytic formula into a Boltzmann solver so that a linear matter power spectrum is readily accessible. Our benchmark model will facilitate FIMP searches and particle physics model-building.
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