在超越標準模型物理中，暗類物質是門有趣的領域。它可能會與標準模型中的粒子產生交互作用，因此我們需要一個媒介來解釋它們之間的交互作用，暗光子則是很好的人選。我們假設暗光子能夠與標準模型中的費米子產生交互作用，且能解釋缈子$g-2$異常。在與標準模型的粒子交互作用中，我們將著重於討論它的衰變。如暗光子之質量大於兩倍電子質量，則暗光子可衰變為輕子對，甚至是更重的強子。許多實驗利用暗光子衰變的特性來搜尋暗光子，並對於暗光子的質量以及其與標準模型粒子的耦合強度設定限制。其中包括對撞機及粒子束陷落實驗，像是BaBar、NA48/2、LHCb、NA64、E137、Orsay、$u$-cal、CHARM等......。除了這些實驗，電子$g-2$同樣對於暗光子設定了限制，$g-2$所限制的區域較無其他實驗限制區域重疊。若是想以暗光子解釋缈子$g-2$異常，其所適用之區域被三個對撞機實驗的限制區域覆蓋。在這篇論文中，我們將會引入另一種假想粒子:類軸子粒子。類軸子粒子是種非常輕的粒子，並有可能與暗光子產生交互作用。暗光子可能會衰變為一個類軸子粒子及一個光子。在類軸子粒子的影響下，原先由實驗所得到的限制區域將會有所改變。若是類軸子粒子的影響足夠強烈，則缈子$g-2$的適用區域將會與其餘實驗的限制區域分開，並能在暗光子質量超過一百億電子伏特時利用暗光子來解釋缈子$g-2$異常。

Dark sector is an interesting topic in physics beyond Standard Model. It is possible that dark sector may interact with Standard Model (SM) particle by $U(1)$ kinetic-mixing. Dark photon is a theoretical particle that corresponding to the interaction between dark sector and SM particle. This particle not only can connect dark sector and SM particle, but also may explain muon $g-2$ anomaly. For massive dark photon, it can decay to SM fermions if its mass heavier than two electron mass. Lots of experiments set the constraints of kinetic-mixing parameter $arepsilon$, such as colliders and beam dump experiments. Collider experiments include BaBar, NA48/2 and LHCb. Beam dump experiments include NA64, E137, Orsay, $
u$-cal, CHARM, etc. $g-2$ also set the constraints of $arepsilon$. Electron $g-2$ covers $arepsilon geq 10^{-4}$ region in $m_{gamma'}-arepsilon$ space, where $m_{gamma'}$ is dark photon mass. The favorite region of muon $g-2$ is set at $arepsilon = 10^{-3}-10^{-2}$, this region is excluded by NA48/2, BaBar and LHCb. In this thesis, we will introduce a light particle, axion-like particle (ALP) $a$, to interact with dark photon. We assume $m_{gamma'} >> m_{a}$, $m_{a}$ is ALP mass, and dark photon can decay to one ALP and one SM photon with coupling $g_{agammagamma'}$. In this assumption, the constraints of dark photon should be changed. With impact of ALP, constraints from collider and beam dump experiments will shift upward and muon $g-2$ favorite region will separate from others constraints. For $g_{agammagamma'} approx 1~m{GeV}^{-1}$, we can use dark photon to explain muon $g-2$ anomaly at $m_{gamma'} >10~m{GeV}$ region.

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