暗物质和宇宙重子数不对称是超出标准模型的两个重要的未解谜团。天文观测数据表明，构成宇宙的物质中有 26.8% 都是暗物质，但是我们对其本质属性仍然所知甚少。新物理在理论上预言了多种暗物质候选者，包括著名的弱相互作用大质量粒子 (WIMPs)、惰性中微子和轴子等等。轴子是超轻暗物质的重要候选者之一，该粒子来自于解释强 CP 问题中 PQ 机制，质量极轻且与普通物质耦合非常弱，无法通过热力学方式产生，对轴子的研究还导致了与其性质相似的类轴子粒子 (ALPs)。实验上，我们一般通过直接探测、间接探测和对撞机探测三种方式来探测暗物质。另一方面，重子数不对称描述了我们所在宇宙中正反物质的不对称性，在早期的宇宙，一些物理过程使得一部分对称性发生破坏，导致现在的物质总量要远远多于反物质总量。近年来，研究表明轴子与重子数不对称之间有密切的联系，因此轴子或类轴子粒子可能在暗物质和重子数不对称两个问题上都发挥重要的作用。基于以上内容，我们在本文中围绕暗物质直接探测、类轴子产生机制和宇宙重子数不对称这三个课题展开研究。

首先，我们讨论利用三体非弹性散射过程来直接探测 sub-MeV 暗物质。由于在传统的两体弹性散射过程中，sub-MeV 量级的暗物质引起的反冲能无法达到目前探测器的阈值，所以直接探测实验对这类轻暗物质的限制很弱。因此我们提出，利用 3→2非弹性散射过程，考虑两个暗物质粒子与目标靶散射，如果初态是两个复标量暗物质，则末态可以形成暗物质束缚态，进而将结合能传递给目标靶粒子；如果初态是两个实标量暗物质，则末态出射一个暗光子，那么两个消耗的暗物质粒子也可以显著提高目标靶的反冲能。我们分别研究了目标靶为原子核和束缚电子的情况，得到了比目前其他直接探测实验更强的对暗光子质量与动力学混合参数的限制，另外还给出了目前部分实验对暗物质--原子核散射截面作为暗物质质量的函数的排除限制，这一过程可以作为传统 2→2 直接探测过程的补充和比较。

然后，我们研究两种不同的类轴子暗物质产生机制，分别在第 I 类和第 II 类跷跷板机制的基础上加入一个携带两个单位轻子数的单态复标量场，其 CP-odd 分量即为整体 U(1)_L 对称性破缺后产生的 Nambu-Goldstone 玻色子，称为 Majoron，我们把该粒子作为类轴子暗物质的候选者。一方面，在扩展的第 II 类跷跷板机制中，Majoron 在电弱相变期间获得质量，然后通过传统 misalignment 机制产生遗迹丰度，其振荡温度存在一个与质量无关的上限值。另一方面，在扩展的第 I 类跷跷板机制中，Majoron 通过与右手中微子相互作用引起的辐射修正获得质量，量子引力导致的轻子数破坏 Majorana 质量项使 Majoron 获得一个非零的初始速度，进而在宇宙早期通过动力学 misalignment 机制产生遗迹丰度。这两类 Majoron 都不存在与双光子的耦合，但是可以通过轻子手征反常诱导的 Majoron--Z 玻色子--光子 (aZγ) 相互作用来进行探测。值得一提的是，在扩展的第 II 类跷跷板机制中，Majoron 可以与标准模型 Higgs 粒子发生混合进而与电子有相互作用，这可以作为探测该粒子的另一种有效方案。

最后，我们考虑在扩展的第 I 类跷跷板机制中产生重子数不对称。我们证明右手中微子的轻子数破坏 Majorana 质量项可以导致最初的轻子数不对称，随后 sphaleron 过程将产生的净轻子数不对称转换为重子数不对称，这一机制能够产生满足目前观测到的宇宙重子数不对称。总之，上述两种方案都仅仅对标准模型做了最小的扩充，却可以在同一理论框架内解释多种新物理现象。

Dark matter and baryon asymmetry of the universe are two important unsolved mysteries beyond the Standard Model. Astronomical data shows that 26.8% of the matter that makes up the universe is dark matter, but we still know very little about its nature. The new physics theoretically predicts a variety of dark matter candidates, including the well-known weakly interacting massive particles (WIMPs), inert neutrinos and axions, etc. Axions are one of the important candidates for ultralight dark matter. It comes from the PQ mechanism that explains the strong CP problem, is extremely light in mass and weakly coupled with ordinary matter, and cannot be produced by thermodynamic methods. The study of axions also leads to the axion-like particles (ALPs) with similar properties. Experimentally, we generally detect dark matter in three ways: direct detection, indirect detection and collider detection. On the other hand, the baryon asymmetry describes the matter-antimatter asymmetry in our universe. In the early universe, some physical processes break some of the symmetries, resulting in the total amount of matter now far more than the total amount of antimatter. In recent years, studies have shown that there is a close connection between axions and baryon asymmetry, so axions or axion-like particles may play an important role in both dark matter and baryon asymmetry. Based on the above, in this paper, we focus on the direct detection of dark matter, the generation mechanism of axion-like particles and the baryon asymmetry of the universe.

First, we discuss the use of a three-body inelastic scattering process to directly detect sub-MeV dark matter. Because the recoil energy caused by sub-MeV dark matter in traditional two-body elastic scattering cannot reach the threshold of current detectors, direct detection experiments have weak constraints on this kind of light dark matter. Therefore, we propose to utilize the 3 → 2 inelastic scattering process by considering the scattering of two dark matter particles with the target. If the initial state is two complex scalar dark matters, the final state can form a dark matter bound state, and then the binding energy can be transferred to the target. If the initial state is two real scalar dark matters, then the final state emits a dark photon, then the two consumed dark matter particles can also significantly increase the recoil energy of the target. We study the cases where the target is the nucleus and the bound electron respectively, and obtain a stronger constraint on the dark photon mass and the kinetic mixing parameter than other direct detection experiments at present. In addition, we also give the exclusion limits on the dark matter-nucleus scattering cross section as a function of dark matter mass for some current experiments. This process can be used as a supplement and comparison to the traditional 2→2 direct detection process.

Then, we study two different axion-like dark matter generation mechanisms, by adding a singlet complex scalar field that carries two units of lepton number to the type-I and type-II seesaw mechanisms, respectively. Its CP-odd component is the Nambu-Goldstone boson after the spontaneous breaking of the global U(1)_L, called Majoron. We consider it as a candidate of axion-like dark matter. On the one hand, in the extended type-II seesaw mechanism, Majoron obtains its mass during the electroweak phase transition and then produces relic abundance through the traditional misalignment mechanism with a mass-independent upper bound of oscillation temperature. On the other hand, in the extended type-I seesaw mechanism, Majoron obtains mass through the radiation corrections induced by the interaction with right-handed neutrinos. The lepton-number-violating Majorana mass term caused by quantum gravity gives Majoron a non-zero initial velocity, which subsequently produces the relic abundance via the kinetic-misalignment mechanism in the early universe. Neither type of Majoron is coupled to di-photons, but it can be detected by the majoron-Z-photon (aZγ) interaction induced by the chiral anomalies of leptons. It is worth mentioning that in the extended type-II seesaw mechanism, Majoron can mix with the Standard Model Higgs and then interact with electrons, which can be used as another effective method to detect this particle.

Finally, we consider the generation of baryon asymmetry in the extended type-I seesaw mechanism. We show that the lepton-number-violating Majorana mass of the right-handed neutrino can lead to an initial lepton asymmetry, which is subsequently transported into the baryon asymmetry of the universe via the sphaleron process. This mechanism can generate a baryon asymmetry that satisfies the currently observed baryon asymmetry of the universe. In short, both scenarios are only the minimal extensions of the Standard Model, but can explain a variety of new physics phenomena within the same theoretical framework.