Abstract
We studied a simple model of hidden sector consists of a Dirac fermion $\chi$ and a spontaneously broken $U(1)_s$ symmetry. The dark sector is connected to the Standard Model(SM) via three righthanded SM singlet neutrinos, $N_R$'s, and the kinetic mixing between $U(1)_s$ and $U(1)_Y$. A mixing between the scalar $\phi$ that breaks $U(1)_s$ and the SM Higgs boson, $H$, is implemented via the term $\phi^\dagger \phi H^\dagger H$ and this provides a third connection to the SM. Integrating out the $N_R$ at a high scale not only gives the active neutrinos, $\nu$, masses but generates effective Dirac type of couplings between $\nu$ and $\chi$. This changes the usual Type-I seesaw results for active neutrino masses and makes $\chi$ behave like a sterile neutrino even though its origin is in the hidden sector. $\chi$ is also split into a pair of Majorana fermions. The amount of splitting depends on the parameters. If the lighter of the pair has a mass around keV, its lifetime is longer than the age of the universe and it can be a warm dark matter candidate. Signatures of $\chi$ in high precision Kurie plots of nuclei $\beta$ decays and low energy neutrino nuclei coherent scatterings are discussed. The model also induces new invisible $Z$ decay modes that can be searched for in future Z factories.
Highlights
Some time ago we investigated a very simple shadow Uð1Þs sector which consists of a scalar φ that spontaneously breaks the gauged Abelian symmetry [1]
We studied a simple model of the hidden sector that consists of a Dirac fermion χ and a spontaneously broken Uð1Þs symmetry
A mixing between the scalar φ that breaks Uð1Þs and the Standard Model (SM) Higgs boson H is implemented via the term φ†φH†H, and this provides a third connection to the SM
Summary
Some time ago we investigated a very simple shadow Uð1Þs sector which consists of a scalar φ that spontaneously breaks the gauged Abelian symmetry [1]. There are claims of the detection of a monochromatic line at 3.56 keV x-ray data towards the Andromeda galaxy and Perseus galaxy cluster in [7,8] This can be interpreted as the radiative decay of a fermion, usually taken to be a sterile neutrino, into an active neutrino plus a photon. The χ fermions in our model appear as a vector pair If they acquire a sizable mass splitting, the lighter one still serves as the WDM while the heavier one is much less restricted than the keV sterile neutrino WDM and could have low energy phenomena. Exploration of this is one of the purposes of this paper.
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