Superheavy Dark Matter with Discrete Gauge Symmetries

We show that there are discrete gauge symmetries protect naturally heavy X particles from decaying into the ordinary light particles in the supersymmetric standard model. This makes the proposal very attractive that the superheavy X particles constitute a part of the dark matter in the present universe. It is more interesting that there are a class of discrete gauge symmetries which naturally accommodate a long-lived unstable X particle. We find that in some discrete Z10 models, for example, a superheavy X particle has lifetime τX ≃ 10 11−1026 years for its mass MX ≃ 10 13−1014 GeV. This long lifetime is guaranteed by the absence of lower dimensional operators (of light particles) couple to the X. We briefly discuss a possible explanation for the recently observed ultra-high-energy cosmic ray events by the decay of this unstable X particle. Research Fellow of the Japan Society for the Promotion of Science. The existence of invisible dark matter in the present universe is one of the central issues in particle physics as well as in astrophysics. Many particle candidates have been, in fact, proposed as constituents of the dark matter. It is usually thought that the dark-matter particles cannot be too heavy, since stable particles much heavier than ∼ 1 TeV would easily overclose the universe if they have been once in thermal equilibrium [1]. Therefore, if one would consider superheavy dark matter, one must invoke, for example, a late-time entropy production to dilute sufficiently the abundance of such superheavy relic particles [2]. This may render this scenario unlikely. Recently, the above problem has been naturally solved by the authors of [3, 4]. They have suggested that inflation in the early universe may generate a desirable amount of such a superheavy particle during the reheating epoch just after the end of inflation. Since the production mechanism for the superheavy particle involves only gravitational interactions, it is quite independent of detailed nature of the particle as well as processes of the reheating. This new observation seems very generic and thus it leads us to consider, in this paper, the proposal that most of the dark matter in the universe indeed consists of some superheavy particles [2]. The numerical calculation in ref. [3] shows that the desired abundance of the superheavy particle X is obtained when its mass MX lies in the region 0.04 < ∼MX/H < ∼ 2 with the Hubble parameter at the end of inflation H ∼ 10 GeV. In this paper, we assume MX ≃ 10 13 − 10 GeV. For the X particle to be a dominant component of the dark matter in the present universe, it must live longer than the age of the universe. Such stability of the superheavy X particle may be explained by imposing some symmetries. We consider here gauge (local) symmetries, since any global symmetries are broken explicitly by topological effects of gravity [5] and the X particle may no longer survive until the present. There are two classes of gauge symmetries, continuous and discrete. We concentrate our discussion on discrete gauge symmetries [7], since analyses for continuous 1 The lifetime of the X particle can be longer than the age of the universe if topological effects of gravity are extremely small [6].