Explaining the 3.5 keV X-ray Line in a ${L_{\mu}-L_{\tau}}$ Extension of the Inert Doublet Model

TL;DR

This paper presents a model extending the inert doublet framework with a gauged $U(1)_{L_{mbda}-L_{ au}}$ symmetry, explaining neutrino masses, dark matter, and the 3.5 keV X-ray line through radiative mechanisms and late decays.

Contribution

It introduces a novel $U(1)_{L_{mbda}-L_{ au}}$ extension of the scotogenic model that accounts for neutrino properties, dark matter, and the X-ray line with a unified radiative and decay-based explanation.

Findings

Two nearly-degenerate RH neutrinos form a two-component dark matter.

The 3.5 keV X-ray line is explained by the decay of the next-to-lightest RH neutrino.

The model naturally generates tiny neutrino masses radiatively.

Abstract

We explain the existence of neutrino masses and their flavor structure, dark matter relic abundance and the observed 3.5 keV X-ray line within the framework of a gauged $U(1)_{L_{\mu} - L_{\tau}}$ extension of the "scotogenic" model. In the $U(1)_{L_{\mu} - L_{\tau}}$ symmetric limit, two of the the RH neutrinos are degenerate in mass, while the third is heavier. The $U(1)_{L_{\mu} - L_{\tau}}$ symmetry is broken spontaneously. Firstly, this breaks the $\mu-\tau$ symmetry in the light neutrino sector. Secondly, this results in mild splitting of the two degenerate RH neutrinos, with their mass difference given in terms of the $U(1)_{L_{\mu} - L_{\tau}}$ breaking parameter. Finally, we get a massive $Z_{\mu\tau}$ gauge boson. Due to the added $Z_2$ symmetry under which the RH neutrinos and the inert doublet are odd, the canonical Type-I seesaw is forbidden and the tiny neutrino masses are generated radiatively at one loop. The same $Z_2$ symmetry also ensures that the lightest RH neutrino is stable and the other two can only decay into the lightest one. This makes the two nearly-degenerate lighter neutrinos a two-component dark matter, which in our model are produced by the freeze-in mechanism via the decay of the $Z_{\mu\tau}$ gauge boson in the early universe. We show that the next-to-lightest RH neutrino has a very long lifetime and decays into the lightest one at the present epoch explaining the observed 3.5 keV line.