Cosmic Ray Positron and Electron Excess from Hidden-Fermion Dark Matter Decays

The anomalies observed in recent cosmic ray experiments seem to strongly constrain the nature of the dark matter. In this letter, we investigate a possibility of the fermionic dark matter with a minimal extension of the standard model. We found that the dark matter decays caused by the dimension six operators can naturally explain the anomalies.


Introduction
The presence of dark matter (DM) has been established by numerous observations, which requires physics beyond the standard model (SM). The nature of the DM is now one of the most important issues not only in cosmology but also in particle physics.
The minimal extension of the SM is to introduce one extra particle called X, that is, a candidate particle for the DM [1]. We assume the DM X to be a singlet of the SM gauge groups. The X particle can be a boson or a fermion. We consider in this letter the case of fermion. We denote the DM X as Ψ to distinguish it from the case of boson 1 .
The new particle Ψ may have Yukawa couplings as which induces too fast decay of the Ψ. Here, ℓ is the lepton doublet, H the Higgs doublet and i = 1, 2, 3 denotes family indices of the leptons. Thus, we assume the Yukawa coupling is strongly suppressed, otherwise the Ψ can not be a candidate of the DM. The required suppression may be easily obtained by suitable configurations of particle wavefunctions in a higher dimensional theory 2 .
If the above dangerous Yukawa coupling constants λ i in Eq. (1) are strongly suppressed as |λ i | ≪ 10 −26 , the dominant operators become dimension six four-Fermi interactions among the SM particles and Ψ: where i, j, k = 1, 2, 3 and M * is the cut-off scale, which would be regarded as the Grand Unification scale. The lifetime of the Ψ is given by where m Ψ is the mass of the DM Ψ. We see that the lifetime is much longer than the age of the universe in a large parameter space of M * and m Ψ and hence the Ψ can be a candidate of the DM.
1 See Refs. [2] for the case of X being a hidden gauge boson A ′ . 2 An example is given in a 5-dimensional space-time with an extra dimension S 1 /Z 2 . We put the Ψ on one boundary and the Higgs H on the other boundary. We put quarks and leptons in the bulk. Then, we find the Yukawa coupling ΨℓH is exponentially suppressed if the size of the extra dimension is large enough, compared with the inverse of the cut-off scale in the 5-dimensional theory.
The Ψ may be produced non-thermally in the early universe through the above dimension six interactions. The density parameter of the Ψ is given by where T R is the reheating temperature after the inflation 3 . We see that the observed DM density Ω DM h 2 ≃ 0.1 is also explained for a wide region of the parameter space of M * , m Ψ and T R .
The purpose of this letter is to show that the anomalous excess of cosmic ray electron and positron recently observed by PAMELA [3] and ATIC [4]/PPB-BETS [5] is naturally explained by the decay of the DM Ψ 4 . In the present analysis we assume the following dimension six operator, for simplicity; where α is a free parameter of O(1). We find that the replacement of the third family by the second family does not significantly change our final result and hence we consider only the above operators. However, the more general analysis including all possible dimension six operators is straightforward and will be given elsewhere.
For completeness, we also study the case that the two-body decays of the DM are induced by Eq. (1). We find that the required lifetime for the DM Ψ is given if the Yukawa couplings |λ i | are sufficiently small as O(10 −26 ). We choose the flavor structure as |λ 1 | ≫ |λ 2,3 | in the present analysis.

Cosmic rays from the hidden fermion DM decays
Let us discuss the cosmic ray signals from the decays of the DM Ψ. The interaction (1) dominantly causes two-body decays of the DM Ψ, with branching ratio 1 : 1 : 2. The interaction (5) mainly causes three-body decays Ψ → τ ± e ∓ ν, e ± e ∓ ν, dbu,dbū with branching ratio 1 : 1 : 3α 2 : 3α 2 . Here, we have assumed that the Ψ is a Majorana fermion and that m h ≃ 110 GeV and m Ψ ≫ m h . In both cases Eqs. (6) and (7), high energy electron, positron, photon and antiproton are produced. To estimate the energy spectrum of these decay products, we have used the program PYTHIA [10]. The particles produced in the DM decays are influenced by various factors in the propagation. For the propagation in the Galaxy, we adopt the method discussed in Refs. [9,11] with Navarro, Frenk and White halo profile [12]; where ρ 0 = 0.26 GeVcm −3 and r c = 20 kpc.

Positrons and electrons
As a diffusion model, we use MED model in Ref. [13]. We see that the positrons and electrons come from the DM decays inside the Galaxy, and especially the decays within a few kpc from us are important. In Fig. 1 Next, we estimate the positron fraction. For the background, we extrapolate the background estimated in Fig. 1 and assume that the background consists entirely of the electron, since the secondary positron would be negligible for E > ∼ 10 GeV. Fig. 2 shows  For the extragalactic component, the gamma ray is influenced by the red-shift. We estimate the extragalactic component by using the following cosmological parameters; [16].
In Fig. 3, the gamma ray fluxes are shown. We set the background flux as 5.18 × 10 −7 (E/1 GeV) −2.499 GeV −1 cm −2 s −1 sr −1 as in Ref. [17]. We have assumed the energy resolution is 15%. In both cases, the DM signals are consistent with the current experiment data and anomalous behavior of the gamma ray flux is expected to continue up to higher energy. This will be tested by upcoming Fermi Gamma-Ray Space Telescope (FGST, formerly named GLAST [18]). Figure 3: Gamma ray fluxes with experimental data [19,20]. Left: three-body decay. Right: two-body decay. Solid line represents the DM signal plus background and dashed the background only.

Antiproton
We estimate the antiproton flux, following the Refs. [9]. For the solar modulation, we set φ F = 500 MV. In Fig. 4, we show the antiproton fluxes for some different diffusion models [13]. Here, we show only the DM signals. We can see the contradiction between the experiments and the signals in some diffusion models. However, in both cases of the two-and three-body decay, MIN models (and also MED model for the three-body decay case) do not conflict with the experimental data. Therefore, for the antiproton, the DM ψ is consistent with the experimental data at least in some diffusion models. Figure 4: Antiproton fluxes with experimental data [21,22]. Left: three-body decay. Right: two-body decay. Solid, dash-dotted and dashed line represent MIN, MED and MAX diffusion models, respectively.

Discussion and conclusions
In this letter, we have investigated the case of the fermionic DM. Both two-and threebody decays can explain the anomaly of electron and positron cosmic ray. In addition, they are also consistent with the gamma ray anomaly. Especially, the decay caused by the dimension six operators seems to be attractive, since it naturally explains the proper lifetime of the DM for the GUT-scale cut-off M * ≃ 10 15 -10 16 GeV 6 .
unclear. In addition, the reason why the DM Ψ decays dominantly into the first family leptons is unclear. However this problem may be solved by choosing suitable Froggatt-Nielsen charge for the DM Ψ 7 .
Finally, we should note that the hidden fermion Ψ can be identified as the lightest neutralino in the supersymmetric standard model. In this case, R-parity breaking operators may induce the DM Ψ decays in similar ways discussed in the present letter.
Note Added: Discrimination between two-and three-body decay of the DM would be possible in the future cosmic ray experiments [26].