[Paper Review] 3.55 keV X-ray Line Interpretation in Radiative Neutrino Model

Hiroyuki Ishida, Hiroshi Okada|arXiv (Cornell University)|Jun 23, 2014

Astrophysics and Cosmic Phenomena12 citations

TL;DR

This paper proposes a radiative neutrino model with a $Z_2 \times Z'_2$ symmetry that explains the 3.55 keV X-ray line anomaly via a keV-scale dark matter fermion ($X_R$) mixing with active neutrinos at two-loop level. The model naturally generates the required tiny mixing angle ($\sim 5 \times 10^{-6}$) and explains the observed X-ray line energy as arising from radiative decay of $X_R$, while simultaneously generating neutrino masses at one-loop level with $\mathcal{O}(1)$ couplings.

ABSTRACT

We discuss the 3.55 keV X-ray line anomaly reported by XMN-Newton X-ray observatory using data of various galaxy clusters and Andromeda galaxy in a radiative neutrino model, in which the mixing between the active neutrino and the dark matter is generated at two-loop level after the spontaneous breaking of $Z_2$ symmetry. It might provide us a natural explanation of its tiny mixing ${\cal O}(10^{-10})$, which is observed by their experiments. Such an Abelian discrete symmetry plays a crucial role in differentiating the TeV scale Majorana field from our dark matter, whose mass is expect to be around 7.1 keV.

Motivation & Objective

• To explain the 3.55 keV X-ray line anomaly observed in X-ray observations of galaxy clusters and the Andromeda galaxy.
• To provide a natural explanation for the extremely small mixing angle ($\sim 10^{-10}$) between dark matter and active neutrinos.
• To realize a keV-scale dark matter candidate ($X_R$) with a long lifetime consistent with cosmological observations.
• To generate the observed neutrino masses via one-loop radiative seesaw mechanism with $\mathcal{O}(1)$ couplings.
• To ensure dark matter stability and avoid conflicts with direct detection constraints through discrete symmetries.

Proposed method

• Introduces two gauge singlet Majorana fermions ($N_R$, $X_R$) and three inert scalars ($\eta_i$, $\chi^+$, $\chi^0$) to the Standard Model with $Z_2 \times Z'_2$ symmetry.
• Uses the $Z_2$ symmetry to stabilize $X_R$ at tree level and $Z'_2$ to forbid tree-level mixing, ensuring two-loop generation of neutrino-DM mixing.
• Constructs a one-loop radiative seesaw mechanism for neutrino mass generation via $N_R$ and $\eta_i$ loops.
• Derives the two-loop mixing term between $X_R$ and active neutrinos using a loop function $F$ involving $M_N$, $m_\ell$, and Yukawa couplings.
• Computes the mixing angle $\theta \approx 5 \times 10^{-6} \times (7.1~\text{keV}/M_X) \times (\mu_{ij}/100~\text{GeV}) \times (y_\chi/\mathcal{O}(1)) \times (F/\mathcal{O}(0.1))$ to match the X-ray line energy.
• Considers $X_R$ production via scalar decays ($\chi^0 \to X_R \bar{X}_R$) or $\chi^+ \to X_R \ell^+$, ensuring relic abundance consistency.

Experimental results

Research questions

• RQ1 Can the 3.55 keV X-ray line anomaly be explained by the radiative decay of a keV-scale dark matter fermion?
• RQ2 How can the extremely small mixing between dark matter and active neutrinos ($\sim 10^{-10}$) be naturally generated?
• RQ3 Can neutrino masses be generated at one-loop level while preserving the required two-loop mixing for the X-ray line?
• RQ4 What role do the $Z_2 \times Z'_2$ symmetries play in stabilizing the dark matter and suppressing unwanted interactions?
• RQ5 Is the model consistent with direct detection constraints and relic abundance observations?

Key findings

• The model successfully explains the 3.55 keV X-ray line as arising from the radiative decay of a 7.1 keV dark matter fermion ($X_R$) via two-loop mixing with active neutrinos.
• The mixing angle $\theta \approx 5 \times 10^{-6}$ is naturally achieved with $\mathcal{O}(1)$ Yukawa couplings and $\mathcal{O}(0.1)$ loop function $F$, avoiding fine-tuning.
• Neutrino masses are generated at one-loop level via the Ma-model seesaw mechanism, with the $N_R$ and $\eta_i$ fields mediating the correction.
• The $Z_2$ symmetry ensures $X_R$ stability at tree level, while $Z'_2$ breaking at $v'$ generates the two-loop mixing, preventing tree-level contributions.
• The model avoids direct detection constraints because the mass splitting between inert scalar states ($\sim$ GeV) is large enough to suppress $Z$-boson exchange processes.
• The relic abundance of $X_R$ can be naturally achieved via scalar or gauge boson decays, consistent with cosmological observations.