粒子物理标准模型(Standard Model, SM)是物理学史上最成功的理论之一，它描述了基本物质组成成分(夸克和轻子)如何通过弱、强和电磁力在微观水平上相互作用。虽然标准模型的预测都被实验一一证实，说明了标准模型的正确性，但是标准模型还面临着很多未解答的问题，比如暗物质(dark matter,DM)问题。天文学对星系以及星系团引力的观测首次给出了暗物质存在的证据，随后大量的宇宙学及天文学观测都证实了暗物质的存在，并且精确测量到暗物质在宇宙中约占总能量的26.8\%。到目前为止我们对暗物质的了解全部来源于引力效应，对其粒子性质知之甚少。我们已知暗物质是一种电中性的、色中性、长寿命的大质量粒子，按照暗物质的这些粒子性质，标准模型中并不存在合适的暗物质候选者，我们需要寻找一些可能的暗物质粒子候选者，暗物质的存在意味着新物理的出现。

为了研究暗物质的性质，物理学家提出了各种各样的模型并给出暗物质的候选者，如超对称模型(Supersymmetry,SUSY)中的“超中性子”、轴子模型中的轴子等。目前最流行的暗物质候选者是弱相互作用大质量粒子(weakly interacting massive particles,WIMPs)，这种粒子的质量在电弱能标附近，并且可以通过freeze-out机制十分自然地解释观测到的暗物质剩余丰度。WIMPs与标准模型粒子之间可以发生弱相互作用，可以通过这种相互作用研究暗物质。

探测WIMPs的方法主要有三种：间接探测、直接探测、对撞机探测。三种探测手段中直接探测是最直接的探测方式，如果探测到暗物质粒子的信号，就可以得到暗物质粒子的质量、散射截面等粒子性质；反之如果探测不到暗物质粒子的信号，就可以对相应的模型参数空间施加严格的限制。计算暗物质粒子与核子的散射截面对于暗物质的探测是非常重要的。

本文考虑了top-philic暗物质简化模型，这种模型对标准模型进行扩展，引入了自旋为1的中间态粒子和Dirac费米子型的暗物质粒子，中间态粒子只与暗物质粒子以及标准模型中的top-quark相互作用，可以将暗物质与标准模型连接起来。在这种模型中，自由参数主要是两种粒子的质量和耦合常数。暗物质主要湮灭到一对top-quark和一对中间态粒子，在小质量区域，我们还考虑了暗物质的三体湮灭过程和通过top-quark圈湮灭到一对胶子的过程，通过已知的暗物质剩余丰度，可以对模型的参数进行限制。除此之外，我们还考虑了直接探测实验对模型参数的限制，在这种模型中，树图阶的暗物质与核子的散射截面是不存在的，根据法雷定理，one-loop的散射截面贡献也为0，因此我们计算了暗物质与核子散射截面的two-loop修正，数值结果表明two-loop修正后的自旋无关散射截面的贡献是非常可观的，对直接探测实验而言具有重要意义。

The Standard Model (SM) of particle physics is one of the most successful theories in the history of physics, It describes how the components of basic matter (quarks and leptons) interact at the microscopic level through weak, strong and electromagnetic forces. Although the predictions of the standard model have been experimentally confirmed, demonstrating its correctness, the standard model still faces many unanswered problems, such as the dark matter (DM) problem. Astronomical observations of the gravity of galaxies and galaxy clusters have provided evidence for the existence of dark matter for the first time. Subsequently, a large number of cosmological and astronomical observations have confirmed the existence of dark matter, and it has been accurately measured that dark matter accounts for approximately 26.8\% of the total energy in the Universe. So far, our understanding of dark matter has all come from the gravitational effect, and little is known about its particle properties. We know that dark matter is an electric neutral, color neutral, and long-lived mass particle. According to the properties of these particles, there is no suitable dark matter candidate in the standard model. We need to look for some possible dark matter particle candidates, and the existence of dark matter implies the emergence of new physics.

In order to study the properties of dark matter, physicists have proposed various models and given dark matter candidates, such as the "neutralino" in the supersymmetry (SUSY) model, the axion in the axion model. The most popular candidate for dark matter at present is weakly interacting massive particles (WIMPs), which have masses near the electroweak scale and can naturally explain the observed relic abundance of dark matter through the freeze-out mechanism. Weak interactions can occur between WIMPs and standard model particles, and dark matter can be studied through these interactions.

There are three main methods for detecting WIMPs: indirect detection, direct detection, and collider detection. Direct detection is the most direct detection method among the three detection methods. If the signal of dark matter particles is detected, the particle properties such as their mass and scattering cross-section can be obtained. If the signal of dark matter particles cannot be detected, strict restrictions can be imposed on the corresponding model parameter space. Calculating the scattering cross-section between dark matter particles and nucleons is crucial for the detection of dark matter.

In the work we consider a simplified model which extends the SM with a spin-1 mediator particle and Dirac Fermion type dark matter particles. Mediator particles only interact with dark matter particles and the top-quark in the standard model, which can connect dark matter with the standard model. In this model, the free parameters are mainly the masses and coupling constants of the two particles. Dark matter mainly annihilates into a pair of top quarks and a pair of intermediate particles. In the small mass region, we also consider the three-body annihilation process of dark matter and the process of annihilating into a pair of gluons through the top-quark loop. By knowing the relic abundance of dark matter, we can constrain the parameters of the model. In addition, we also considered the limitations of direct detection experiments on model parameters,In this model, the scattering cross sections of dark matter and nucleons in the tree-level do not exist. According to Farry's theorem, the scattering cross section contribution of one-loop is also 0. Therefore, we calculated the two-loop correction of the scattering cross sections of dark matter and nucleons.The numerical results show that the contribution of the spin-independent scattering cross section with inclusion of the two-loop correction is very significant.It is of great significance for direct detection experiments.