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The KSVZ Axion and Pseudo-Nambu-Goldstone Boson Models for the XENON1T Excess

The XENON1T excess can be explained by the Axion Like Particle (ALP) dark matter with mass around 2.5 keV. However, there are three problems needed to be solved: suppressing the coupling $g_{aγ}$ between the ALP and photon, and generating the proper coupling $g_{ae}$ between the ALP and electron as well as the correct ALP mass. We propose three models to solve these problems. In our models, the $g_{ae}$ couplings are produced by integrating out the vector-like leptons, and the correct ALP masses arise from high-dimensional operators. In the KSVZ axion model, the coupling $g_{aγ}$ can be suppressed by choosing proper sets of vector-like fermions, but we need some fine-tunings to obtain the ALP mass. Similarly, one can study the DFSZ axion model. In the $Z_8$ and $ U(1)_X$ models with approximate Pseudo-Nambu-Goldstone Bosons (PNGBs), the coupling $g_{aγ}$ is suppressed due to $SU(3)_C \times U(1)_{\rm EM}$ anomaly free. In the $Z_8$ model, the PNGB mass can be generated naturally at the keV scale via the dimension-8 operator. To solve the PNGB quality problem in the $ Z_8$ model, we embed it into the model with $ U(1)_X$ gauge symmetry.