Radiatively decaying scalar dark matter through U(1) mixings and the Fermi 130 GeV gamma-ray line

Abstract

In light of the recent observation of the Fermi-LAT 130 GeV gamma-ray line, we suggest a model of scalar dark matter in a hidden sector, which can decay into two (hidden) photons. The process is radiatively induced by a GUT scale fermion in the loop, which is charged under a hidden sector U(1), and the kinetic mixing ($\sim ϵF^{\mu \nu }{F}_{\mu \nu }^{\prime }$) enables us to fit the required decay width for the Fermi-LAT peak. The model does not allow any dangerous decay channels into light standard model particles.

Introduction

Although the major constituent of matter content of the Universe is dark matter (DM), we only know little about its nature so far [1]. Having no DM candidate in its particle contents, the standard model (SM) is strongly required to be extended. One intriguing possibility is that a hidden sector attached to the standard model sector includes a dark matter candidate. The singlet DM candidate could be a scalar [2], a fermion [3], [4], [5] or a vector boson [6], [7].

The recent claim of the Fermi Large Area Telescope (Fermi-LAT) [8] 130 GeV γ-ray line [9], [10] shed light on further details of the dark matter property since no known astrophysical source would produce such a peak. The claim was further strengthened by [11] (and also [12], [13]) even though the Fermi-LAT Collaboration only has provided sensitivity limits on dark matter models based on a part of the acquired data set on different region of interest [14] (also see [15]). There are explanations of this γ-ray line based on spectral and spatial variations of diffuse γ-ray [16] and new background with ‘Fermi-bubble’ [17], but the most interesting interpretation might be that the γ-ray line could be originated from the DM annihilation, $\chi \chi \to \gamma \gamma [\text{or}\gamma X]$ with $E_{\gamma }\simeq m_{\chi }[\text{or}{m}_{\chi }(1-m_X^2/4m_{\chi }^2)]\simeq 130\text{GeV}$ [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] or the DM decay, $\chi \to \gamma \gamma [\text{or}\gamma X]$ with $2E_{\gamma }\simeq m_{\chi }[\text{or}{m}_{\chi }(1-m_X^2/m_{\chi }^2)]\simeq 260\text{GeV}$ [28], [31].¹

For the DM annihilation interpretation of the 130 GeV γ-ray peak, the required values for annihilation cross section is found to be ${〈\sigma v〉}_{\chi \chi \to \gamma \gamma }\sim \mathit{a}\mathit{f}\mathit{e}\mathit{w}\times {10}^{-27}{\text{cm}}^3/\text{s}$,² which is approximately one order of magnitude smaller than the total annihilation cross section for the thermal production of DM, ${〈\sigma v〉}_{\chi \chi \to \mathit{SM}}\simeq 3\times {10}^{-26}{\text{cm}}^3/\text{s}$ [1]. As the dark matter is likely to be electrically neutral (or milli-charged [4], [5], [37]), the annihilation process for γγ production may be radiatively induced by massive charged particles in the loop. If some of the charged particles are lighter than the DM particle, there could appear tree-level annihilation channels to these charged particles, which may dominantly determine the relic abundance of dark matter. However, the loop factor is too small as $g^2/16{\pi }^2\lesssim {10}^{-2}$ and thus does not correctly account the discrepancy between the cross sections. A variety of annihilating DM models have been suggested to overcome this issue [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30].

Decaying DM can be an alternative explanation. Indeed, decaying dark matter models have been recently proposed to account the excessive observation of positron in the PAMELA and ATIC where the dark matter is a vector boson in a hidden sector [7]. The vector boson of the hidden sector Abelian gauge group $\mathrm{U}{(1)}^{\prime }$ can decay to the standard model photon through the kinematical mixing term $ϵF_{\mu \nu }{F}^{\prime \mu \nu }$, where $F^{\mu \nu }(F^{\prime \mu \nu })$ is the field strength tensor of $\mathrm{U}(1)$ ($\mathrm{U}{(1)}^{\prime }$) gauge boson, respectively. As the mixing parameter could be small ($ϵ\sim {10}^{-26}$) [7], the decay width could be suppressed. However, the decay of a vector boson to a pair of photons is forbidden by the Landau–Yang theorem [38] so that we need another model. In Refs. [28], [31], a scalar dark matter, ϕ, was considered with an effective operator allowing the decay to two photons: $c_6\frac{\varphi \varphi }{{\Lambda }^2}{F}^{\mu \nu }{F}_{\mu \nu }$, which is dimension six.³ It is pointed out in Ref. [31] that a dimension five operator, $c_5\frac{\varphi }{\Lambda }{F}^{\mu \nu }{F}_{\mu \nu }$, cannot fit the data without introducing trans-Planckian cutoff ($\Lambda \gg M_{Pl}$) or equivalently a largely suppressed coefficient $c_6\ll 1$ as the required partial decay width of the dark matter to photons is extremely small, $\Gamma (\varphi \to \gamma \gamma )\sim {10}^{-29}{s}^{-1}$.

In this Letter, we try to combine the advantages of above two cases:

• A scalar dark matter can decay into γγ differently from the massive vector dark matter,

• A small kinetic mixing ϵ can make the effective couplings of the dark matter particle with the standard model particles small.

Combining these two advantages, we suggest a dark matter model, which has an effective dimension five operators of the form:

$$\mathcal{O}=c_5\frac{\varphi }{\Lambda }(F_{\mu \nu }^{\prime }{F}^{\prime \mu \nu }+ϵF_{\mu \nu }{F}^{\prime \mu \nu }+{ϵ}^2{F}_{\mu \nu }{F}^{\mu \nu }),$$

from which we can learn that the decay amplitudes to $\gamma {\gamma }^{\prime }$ and γγ are relatively suppressed by a factor of ϵ and ${ϵ}^2$ with respect to the one for ${\gamma }^{\prime }{\gamma }^{\prime }$ channel due to the mixing.

In the next section (Section 2), we further explain the model in detail and present the partial decay widths of the dark matter to (hidden) photons then clarify the model parameter space providing a good fit to the 130 GeV gamma-ray line. Discussions on possible experimental bounds on the same parameter space follow. In Section 4, we further discuss the theoretical issues concerning the consistency of the model and also other cosmological observations then conclude in Section 5. Finally, in Appendix A, we present some details of the U(1) mixing Lagrangian for an extra unbroken U(1) symmetry.