Neutrinos continue to provide a testing ground for the structure of the standard model of particle physics as well as hints towards the physics beyond the standard model. Neutrinos of energies spanning over several orders of magnitude, originating in many terrestrial and astrophysical processes, have been detected via various decay and interaction mechanisms. At MeV scales, there has been one elusive process, until a few years ago, known as coherent elastic neutrino-nucleus scattering (CEvNS) that was theoretically predicted over five decades ago but was never observed experimentally. The recent experimental observation of the CEvNS process by the COHERENT collaboration at a stopped pion neutrino source has inspired physicists across many subfields. This new way of detecting neutrinos has vital implications for nuclear physics, high-energy physics, astrophysics, and beyond. CEvNS, being a low-energy process, provides a natural window to study light, weakly-coupled, new physics in the neutrino sector. Leveraging orders of magnitude higher CEvNS cross section, new physics can be searched with relatively small detectors.

In this review, we intend to provide the current status of low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics. We discuss low energy sources of neutrinos with a focus on neutrinos from the stopped pions. Stopped pion sources cover energies in the tens of MeVs and are almost optimal for studying CEvNS. Several worldwide experimental programs have been or are being set up to detect CEvNS and new physics signals in the near future with complementary detection technologies and physics goals. We discuss the general formalism of calculating the tree-level CEvNS cross section and the estimated theoretical uncertainties on the CEvNS cross section stemming from different sources. We also discuss the inelastic scattering of tens of MeV neutrinos that have implications for supernova detection in future neutrino experiments. The stopped-pion facilities are also a near-ideal tens of MeV neutrino source to study inelastic neutrino-nucleus cross sections. We discuss how the CEvNS experiments can be used as a testing ground for the Standard Model (SM) weak physics as well as in searching for the Beyond the Standard Model (BSM) physics signals. Any deviation from the SM predicted event rate either with a change in the total event rate or with a change in the shape of the recoil spectrum, could indicate new contributions to the interaction cross-section. The SM implications include the study of weak nuclear form factor and weak mixing angle. The BSM studies include non-standard interactions, neutrino electromagnetic properties, and sterile neutrino searches. Stopped pion facilities are also a copious source of neutral and changed mesons that allow study of several dark sector physics scenarios such as vector portal models, leptophobic dark matter as well as axion-like particle searches.

中微子继续为粒子物理标准模型的结构提供试验场，并为标准模型之外的物理提供线索。起源于许多陆地和天体物理过程的能量跨越几个数量级的中微子已经通过各种衰变和相互作用机制被检测到。在 MeV 尺度上，直到几年前，还存在一种难以捉摸的过程，称为相干弹性中微子核散射 (CEvNS)，它在 50 多年前就在理论上被预测过，但从未在实验中观察到。最近，COHERENT 合作在停止的 π 中微子源上对 CEvNS 过程进行了实验观察，这给许多子领域的物理学家带来了启发。这种检测中微子的新方法对核物理学、高能物理学、天体物理学等具有重要意义。CEvNS 是一种低能过程，为研究中微子领域的光、弱耦合新物理提供了一个天然的窗口。利用高几个数量级的 CEvNS 横截面，可以使用相对较小的探测器来搜索新的物理现象。

在这篇综述中，我们打算提供低能中微子散射物理学的现状及其对标准和标准模型物理学之外的影响。我们讨论中微子的低能量来源，重点关注来自停止的介子的中微子。停止的 π 介子源涵盖了数十 MeV 的能量，几乎是研究 CEvNS 的最佳选择。多个世界范围的实验计划已经或正在建立，以在不久的将来通过互补的检测技术和物理目标来检测 CEvNS 和新的物理信号。我们讨论了计算树级 CEvNS 横截面的一般形式以及来自不同来源的 CEvNS 横截面的估计理论不确定性。我们还讨论了数十 MeV 中微子的非弹性散射，这对未来中微子实验中的超新星探测具有影响。停止的π介子设施也是研究非弹性中微子核横截面的近乎理想的数十兆电子伏中微子源。我们讨论了如何将 CEvNS 实验用作标准模型 (SM) 弱物理的试验场以及如何寻找超越标准模型 (BSM) 的物理信号。任何与 SM 预测事件发生率的偏差，无论是随着总事件发生率的变化还是随着反冲谱形状的变化，都可能表明对相互作用截面的新贡献。SM 的意义包括弱核形状因子和弱混合角的研究。BSM 研究包括非标准相互作用、中微子电磁特性和惰性中微子搜索。停止的介子设施也是中性介子和变化介子的丰富来源，可以研究多种暗区物理场景，例如矢量门户模型、疏疏暗物质以及类轴子粒子搜索。