The inert doublet model is a minimal dark matter model with strong theoretical motivations, where the stability of dark matter is usually achieved by imposing a $Z_2$ parity. We promote the $Z_2$ parity into a global $U(1)$ symmetry and study its phenomenological implications. There are two characteristic features of the model: both the CP-even and CP-odd neutral inert scalars, $h_1$ and $h_2$, become DM candidates; the number of model parameters is one less than that with $Z_2$ parity. We first analyze the constraints from LEP experiments, electroweak precision tests, theoretical stability, Higgs precision data, dark matter relic density, and direct detection experiments. It is found that if the model is required to explain at least 10% of the observed relic density, the theory is extremely limited such that the dark matter mass is about $70\;{\rm GeV}$ and the charged Higgs boson is not very heavy. Focusing on this narrow parameter space, we calculate the production cross sections of almost all the possible mono-$X$ and mono-$XX\prime$ processes at the LHC. The mono-$W\gamma$ process is shown to have high discovery potential with the help of the decay of the intermediate-mass charged Higgs boson into $W^{\pm }{h}_{1,2}$. A search strategy is designed to increase the potential discovery of the model for the mono-$W\gamma$ signal at both the HL-LHC and the FCC-hh. The optimal cut on $E_T^{\rm miss}/\sqrt{H_T}$ is suggested to maximize the signal significance, being about $0.76$ at the HL-LHC and about $7.5$ at the FCC-hh.

中文翻译：

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具有整体U（1）对称性的惰性二重态模型的现象学

惰性二重态模型是具有强烈理论动机的最小暗物质模型，其中暗物质的稳定性通常是通过施加 ${ž}_2$平价。我们推广${ž}_2$ 成为全球平价 $ü（\mathrm{1个}）$对称性并研究其现象学意义。该模型具有两个特征：CP均值和CP奇数中性惰性标量，$H_{\mathrm{1个}}$ 和 $H_2$，成为DM候选人；模型参数的数量比${ž}_2$平价。我们首先分析来自LEP实验，电弱精度测试，理论稳定性，希格斯精度数据，暗物质残留物密度和直接检测实验的约束条件。发现如果需要模型解释至少10％的观测文物密度，则该理论极为有限，以致暗物质质量约为$ 70 \; {\ rm GeV} $，而带电的希格斯玻色子不是非常重。针对这一狭窄的参数空间，我们计算了几乎所有可能的单$X$ 和单声道$XX\prime$LHC的流程。单声道$\mathrm{w\; ^}\gamma$ 中间质量带电的希格斯玻色子的衰变有助于证明该过程具有很高的发现潜力。 ${\mathrm{w\; ^}}^{\pm }{H}_{\mathrm{1个}，2}$。搜索策略的设计旨在增加对单模型的潜在发现$\mathrm{w\; ^}\gamma$HL-LHC和FCC-hh都发出信号。建议对$ E_T ^ {\ rm miss} / \ sqrt {H_T} $进行最佳切割，以最大程度地提高信号的重要性，约为$0.76$ 在HL-LHC和 $7.5$ 在FCC-hh。