标准模型在描述基本粒子及其相互作用方面取得了显著成功，但目前仍然 面临一些挑战，如中微子质量、暗物质的粒子性质和轻子味普适性违反等。因此， 我们需要超出标准模型的新物理理论来解释相关问题。在探索新物理时，通常有 两种方法：一种方法是专注于特定的新物理模型，其中包括引入新粒子或扩展标 准模型的相互作用。另一种常用的方法则是利用有效场论，使用模型无关的高量 纲算符来描述量子效应，而不受特定物理模型的限制。具体研究工作包括： 首先，我们将专注于在低能轻子对撞机(如Belle II 和STCF) 上研究+− → +− 过程所包含的新物理；重点探讨了包含轻子味普适性违反以及描述偶极矩 相互作用的有效算符对标准模型的影响。在使用极化+− 束流的情况下，提取 新物理与标准模型之间干涉项对于方位角不对称性可观测量的贡献。特别关注 了那些在非极化初态束流的情况下与标准模型不存在干涉项的算符。在低能有 效场论(LEFT) 的框架下，目前的实验通过对电子电偶极矩(EDM) 和磁偶极矩 (MDM) 的精密测量，已经间接地对相应算符的威尔逊系数施加了较强的限制。然 而，通过EDM 和MDM 给出的间接约束可能受到算符之间的相互关联以及潜在 新物理的影响。在我们的工作中，强调了直接给出单个算符限制的必要性。同时 在标准模型有效场论(SMEFT) 的框架下，我们从低能有效场论的结果通过“匹 配”给出了相应SMEFT 算符的限制结果。 其次，我们利用亲顶夸克暗物质简化模型(Top-Philic DM Simplified Model) 来探索暗物质的粒子性质。此处对标准模型进行简单的扩展，引入了两种新的粒 子：满足2 对称性的暗物质粒子和矢量型中间态粒子(传递暗物质与顶夸克之 间的相互作用)。针对暗物质湮灭过程，我们利用当前实验给出的暗物质剩余丰 度，对暗物质、顶夸克和中间态粒子之间的相互作用耦合常数给出了一定的限制 范围。在暗物质质量较小的情况下，研究中特别强调了由顶夸克圈到一对胶子的 圈图诱导过程 (̄ → )̄ 和相应三体过程 (̄ → ̄−) 的重要性，并提供了符 合暗物质剩余丰度的参数空间。在直接探测暗物质的过程中，树图阶和一圈散射 过程对于自旋无关散射截面并没有贡献。因此，我们通过使用高量纲算符来描述 暗物质与胶子之间的相互作用，计算暗物质与核子的自旋无关散射截面的两圈 修正。 最后，对中微子新物理进行的研究主要关注于中微子振荡。在 − 模型 中，探讨了狄拉克暗物质的现象学，以及暗物质晕中中微子的振荡行为。详细分析了在暗物质晕中物质效应对中微子质量、轻子混合角、狄拉克 相位以及中 微子振荡几率的影响。 通过对轻子味普适性违反、暗物质粒子性质以及中微子振荡等方面的研究， 我们在不同能级和物理过程中取得了显著的新物理探索进展。这些研究为我们 更深入地理解超出标准模型的新物理现象提供了重要的启示。

The Standard Model has made remarkable achievements in describing elementary particles and their interactions, but it still faces some challenges, such as neutrino mass, particle properties of dark matter, and leptonic flavor universality violations. Therefore, we need theories beyond the scope of the standard model to explain these problems. When exploring new physics, there are usually two approaches: One is to focus on a specific new model of physics, which involves introducing new particles or extending the interactions of the Standard Model. Another common approach is to use effective field theory, which uses model-independent higher-order operators to describe quantum effects without being constrained by a particular physical model. Specific research work includes: First, we will focus on studying +− → +− processes at low-energy lepton colliders such as Belle II and STCF. Then, the effect of the effective operator of Dim-6 involving the violation of lepton flavor universality and describing the dipole moment interaction on the standard model is discussed in detail. In the case of a polarized +− beam, the contribution of the interference terms between the new physics and the Standard Model to the azimuth asymmetry distribution is extracted. Special attention is paid to operators that have no interference terms with the standard model in the case of non-polarized initial state beams. Under the framework of low energy effective field theory (LEFT), the present experiments have indirectly imposed strong constraints on the Wilson coefficients of the corresponding operators through precise measurements of the electronic electric dipole moment (EDM) and magnetic dipole moment (MDM). However, the indirect constraints given by EDM and MDM can be affected by the intercorrelations between operators and potentially new physics. In our work, we emphasize the necessity of directly giving a single operator constraint. At the same time, under the framework of Standard Model effective field theory (SMEFT), we give the limited results of the corresponding SMEFT operators from the results of low energy effective field theory by “matching”. Secondly, we use the Top-Philic DM Simplified Model to explore the particle properties of dark matter. Here, a simple extension of the Standard Model is made to introduce two new types of particles: dark matter particles satisfying the symmetry of 2 and vector intermediate particles. For the dark matter annihilation process, we use the residual abundance of dark matter given by the current experiment to give a certain limit to the interaction coupling constant between dark matter, top quarks and intermediate particles. In the case of the low mass of dark matter, the importance of the loop-induced process from the top quark cycle to a pair of gluons (̄ → )̄ and the corresponding three-body process (̄ → ̄−) is particularly emphasized, and the parameter space consistent with the relic abundance of dark matter is provided. In the process of direct detection of dark matter, the tree order and the one-loop scattering process do not contribute to the spin-independent scattering cross section. Therefore, we calculate a two-loop correction of the dark matter spin-independent scattering cross section of nucleons by using high-dimensional operators to describe the interaction between dark matter and gluons. Finally, research into the new physics of neutrinos focuses on neutrino oscillations. In the − model, the phenomenology of Dirac dark matter and the oscillatory behavior of neutrinos in the dark matter halo are discussed. The effects of matter effect on neutrino mass, lepton mixing Angle, Dirac phase and neutrino oscillation probability in dark matter halo are analyzed in detail. Overall, significant progress has been made in exploring new physics across different energy scales and physical processes through studies of lepton flavor violation, direct detection of dark matter, and neutrino oscillations. These investigations have provided important clues for a deeper understanding of phenomena beyond the Standard Model.