The dark matter may consist not of one elementary particle but of different species, each of them contributing a fraction of the observed dark matter density. A major theoretical difficulty with this scenario --dubbed multi-component dark matter-- is to explain the stability of these distinct particles. Imposing a single $Z_N$ symmetry, which may be a remnant of a spontaneously broken $U(1)$ gauge symmetry, seems to be the simplest way to simultaneously stabilize several dark matter particles. In this paper we systematically study scenarios for multi-component dark matter based on various $Z_N$ symmetries ($N\leq 10$) and with different sets of scalar fields charged under it. A generic feature of these scenarios is that the number of stable particles is not determined by the Lagrangian but depends on the relations among the masses of the different fields charged under the $Z_N$ symmetry. We explicitly obtain and illustrate the regions of parameter space that are consistent with up to five dark matter particles. For $N$ odd, all these particles turn out to be complex, whereas for $N$ even one of them may be real. Within this framework, many new models for multi-component dark matter can be implemented.

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来自 ZN 对称性的多组分标量暗物质：系统分析

暗物质可能不是由一个基本粒子组成，而是由不同的物种组成，它们中的每一个都贡献了观察到的暗物质密度的一小部分。这种被称为多组分暗物质的场景的一个主要理论困难是解释这些不同粒子的稳定性。施加单个 $Z_N$ 对称性，这可能是自发破坏的 $U(1)$ 规范对称性的残余，似乎是同时稳定多个暗物质粒子的最简单方法。在本文中，我们系统地研究了基于各种 $Z_N$ 对称性 ($N\leq 10$) 和不同的标量场集的多组分暗物质场景。这些场景的一个一般特征是稳定粒子的数量不是由拉格朗日量决定的，而是取决于在 $Z_N$ 对称下充电的不同场的质量之间的关系。我们明确地获得并说明了与多达五个暗物质粒子一致的参数空间区域。对于 $N$ 奇数，所有这些粒子都被证明是复杂的，而对于 $N$ 来说，甚至其中一个可能是真实的。在这个框架内，可以实现多组分暗物质的许多新模型。