Radiative neutrino mass and 3.5 keV X-ray line

We consider an extension of Zee-Babu model to explain the smallness of neutrino masses. (1) We extend the lepton number symmetry of the original model to local $B-L$ symmetry. (2) We introduce three Dirac dark matter candidates with flavor-dependent $B-L$ charges. After the spontaneous breaking of $B-L$, a discrete symmetry $Z_6$ remains, which guarantees the stability of dark matter. Then the model can explain the 3.5 keV X-ray line signal with decaying dark matter. We also introduce a real scalar field which is singlet under both the SM and $U(1)_{B-L}$ and can explain the current relic abundance of the Dirac fermionic DMs. If the mixing with the SM Higgs boson is small, it does not contribute to DM direct detection. The main contribution to the scattering of DM off atomic nuclei comes from the exchange of $U(1)_{B-L}$ gauge boson, $Z$, and is suppressed below current experimental bound when $Z$ mass is heavy ($gtrsim 10$ TeV). If the singlet scalar mass is about 0.1--10 MeV, DM self-interaction can be large enough to solve small scale structure problems in simulations with the cold DM, such as, the core-vs-cusp problem and too-big-to-fail problem.

3.5 keV X-ray Line Signal from Dark Matter Decay in Local $U(1)_{B-L}$ Extension of Zee-Babu Model

We consider a local $U(1)_{B-L}$ extension of Zee-Babu model to explain the recently observed 3.5 keV X-ray line signal. The model has three Standard model (SM)-singlet Dirac fermions with different $U(1)_{B-L}$ charges. A complex scalar field charged under $U(1)_{B-L}$ is introduced to break the $U(1)_{B-L}$ symmetry. After $U(1)_{B-L}$ symmetry breaking a remnant discrete symmetry stabilizes the lightest state of the Dirac fermions, which can be a stable dark matter (DM). The second lightest state, if mass splitting with the stable DM is about 3.5 keV, decays dominantly to the stable DM and 3.5 keV photon through two-loop diagrams, explaining the X-ray line signal. Two-loop suppression of the decay amplitude makes its lifetime much longer than the age of the universe and it can be a decaying DM candidate in large parameter region. We also introduce a real scalar field which is singlet under both the SM and $U(1)_{B-L}$ and can explain the current relic abundance of the Dirac fermionic DMs. If the mixing with the SM Higgs boson is small, it does not contribute to DM direct detection. The main contribution to the scattering of DM off atomic nuclei comes from the exchange of $U(1)_{B-L}$ gauge boson, $Z$, and is suppressed below current experimental bound when $Z$ mass is heavy ($gtrsim 10$ TeV). If the singlet scalar mass is about 0.1-10 MeV, the DM self-interaction can be large enough to solve small scale structure problems in simulations with the cold DM, such as, the core-vs-cusp problem and too-big-to-fail problem.

The 3.5 keV X-ray line signature from annihilating and decaying dark matter in Weinberg model

Recently two groups independently observed unidentified X-ray line signal at the energy 3.55 keV from the galaxy clusters and Andromeda galaxy. We show that this anomalous signal can be explained in annihilating dark matter model, for example, fermionic dark matter model in hidden sector with global $U(1)_X$ symmetry proposed by Weinberg. There are two scenarios for the production of the annihilating dark matters. In the first scenario the dark matters with mass 3.55 keV decouple from the interaction with Goldstone bosons and go out of thermal equilibrium at high temperature ($>$ 1 TeV) when they are still relativistic, their number density per comoving volume being essentially fixed to be the current value. The correct relic abundance of this warm dark matter is obtained by assuming that about ${cal O}(10^3)$ relativistic degrees of freedom were present at the decoupling temperature or alternatively large entropy production occurred at high temperature. In the other scenario, the dark matters were absent at high temperature, and as the universe cools down, the SM particles annihilate or decay to produce the dark matters non-thermally as in `freeze-in scenario. It turns out that the DM production from Higgs decay is the dominant one. In the model we considered, only the first scenario can explain both X-ray signal and relic abundance. The X-ray signal arises through $p$-wave annihilation of dark matter pair into two photons through the scalar resonance without violating the constraints from big bang nucleosynthesis, cosmic microwave background, and astrophysical objects such as red giants or white dwarfs. We also discuss the possibility that the signal may result from a decaying dark matter in a simple extension of Weinberg model.

Hidden Sector Dark Matter with Global $U(1)_X$-symmetry and Fermi-LAT 130 GeV $gamma$-ray Excess

We suggest a dark matter scenario which could contribute the possible anomaly observed by Fermi-LAT $gamma$-ray space telescope. It is based on the model recently proposed by Weinberg. In our scenario the gamma-ray line signal comes from the fermionic dark matter ($M_{rm DM}=214 $ GeV) annihilating into two light scalars with mass around 500 MeV which in turn decay into two neutral pions. Finally the pions can decay into two 130 GeV photons. The strong constraint from the direct detection leaves only the channel of the dark matter annihilation into two light scalars for both the relic density and the Fermi-LAT gamma-ray line signal. The resulting gamma-ray spectrum is rather broad and does not fit to the data perfectly, but the data also show there may be fluctuation in the spectrum. There is no associated $Z$-boson or Higgs boson production contrary to most other works where the signal comes from the loops of charged particles. The annihilation into the other SM particles are highly suppressed due to the small mixing from the direct detection. Future experiments with more data will give more clues on the possible scenarios.