Multi-component scalar dark matter from a ZN symmetry: a systematic analysis

Abstract

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 ≤ 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.

The Z5 model of two-component dark matter

“…The Z 5 model can be seen as a natural extension of these scenarios and has the advantage of remaining viable at low masses and of being testable via direct detection experiments. The Z 5 symmetry used in our model is the lowest Z N compatible with two dark matter particles that are complex scalar fields 2 [12]. Even if other Z N symmetries, with N > 5, can be imposed to simultaneously stabilize two dark matter particles [13], the Z 5 model serves as a prototype for all the two-component scenarios where the dark matter particles are complex scalars.…”

“…Let us denote the two dark matter particles charged under a Z N by φ i , φ j (with i < j ≤ N/2 and j = N/2 for N even [12]), where φ k gets a factor e i2πk/N upon a Z N transformation. For 5 < N ≤ 10, the complete set of possibilities for the two dark matter particles is:…”

“…Let us consider a scenario with two new complex scalar fields, φ 1,2 , charged under a Z 5 symmetry. The unique charge assignment (up to trivial field redefinitions) that allows both fields to be stable is [12] φ 1 ∼ ω 5 , φ 2 ∼ ω 2 5 ; ω 5 = exp(i2π/5). (2.1)…”

“…Finally, let us comment on possible extensions of the Z 5 model. A simple one is to embed the Z 5 symmetry within an spontaneously broken U(1) gauge symmetry [12,37]. In that case, the µ S1 term would still be allowed whereas the µ S2 would require an additional vacuum expectation value.…”

“…This symmetry, in turn, could be a remnant of a spontaneously broken U(1) gauge symmetry and thus be related to gauge extensions of the SM. Recently, these scenarios were systematically analyzed [12] and it was found that, surprisingly, their dark matter phenomenology has yet to be investigated in detail. With this paper, we intend to partially fill that gap.…”