AI 中文总结
本文针对亚GeV暗物质的声子探测通道，引入对数哈尔小波基并开发VectorPhonoDark软件包，大幅降低计算成本，实现高效的暗物质模型与探测策略扫描。
AI 中文摘要
晶体中的声子激发是亚GeV暗物质（DM）的一种有前景的探测通道，各向异性靶标可通过速率的日调制提供方向敏感性。利用这些能力需要计算跨暗物质模型、靶材料、探测器取向和一天中不同时间的六维速率积分。矢量空间积分方法将计算分解为暗物质速度分布和材料响应的投影（各计算一次并重复使用），再与解析运动学矩阵收缩，将此类扫描简化为快速矩阵代数。然而，在声子通道中，相关动量转移跨度达六个数量级，现有实现采用的线性间隔哈尔小波基存在不足：轻媒介模型需要大到不切实际的基，且跨暗物质质量重复使用单个投影会损失轻暗物质的有效分辨率。我们引入一种对数哈尔小波基，解决了这两个问题，并提供了实现该方法的软件包VectorPhonoDark。在Al₂O₃的日调制基准测试中，它重现了PhonoDark直接数值积分的结果，同时将计算成本降低了多个数量级。尽管此处为声子开发，但对数小波基可推广到任何跨宽动量转移范围的暗物质探测通道，支持对暗物质模型和探测策略的高效扫描。
英文摘要
Phonon excitations in crystals are a promising detection channel for sub-GeV dark matter (DM), and anisotropic targets add directional sensitivity through the daily modulation of the rate. Exploiting these capabilities requires evaluating six-dimensional rate integrals across DM models, target materials, detector orientations, and times of day. The vector space integration method factorizes the calculation into projections of the DM velocity distribution and of the material response -- each computed once and reused -- contracted with an analytic kinematic matrix, reducing such scans to fast matrix algebra. In the phonon channel, however, the relevant momentum transfers span six orders of magnitude, and the linearly spaced Haar wavelet basis of existing implementations falls short: light mediator models demand an impractically large basis, and a single projection reused across DM masses loses its effective resolution for light DM. We introduce a logarithmic Haar wavelet basis that resolves both obstacles, and present a package VectorPhonoDark that implements the approach. On an Al$_2$O$_3$ daily modulation benchmark, it reproduces results from PhonoDark's direct numerical integration while reducing the computational cost by orders of magnitude. Though developed here for phonons, the logarithmic wavelet basis generalizes to any DM detection channel spanning a wide range of momentum transfers, enabling efficient scans over DM models and detection strategies.
Comments33 pages, 6 figures, 9 tables; VectorPhonoDark available at https://github.com/xuxiangli/VectorPhonoDark
