Right-handed (RH) Majorana neutrinos play a crucial role in understanding the origin of neutrino mass, the nature of dark matter and the mechanism of matter-antimatter asymmetry. In this work, we investigate the observability of heavy RH Majorana neutrino through the top quark neutrinoless double beta decay process t → bℓ + ℓ + jj ′ (ℓ = e, µ) at hadron colliders. By performing detector level simulation, we demonstrate that the heavy neutrinos with the mixing parameters |VeN,µN | 2 5 × 10 −6 in the mass range of 15 GeV < mN < 80 GeV can be excluded at 2σ level at 13 TeV LHC with the luminosity of 36 fb −1 , which is stronger than other existing collider bounds. The future HL-LHC will be able to further probe the mixings |VeN,µN | 2 to about 1.4 × 10 −6 .

In a previous work we showed that keV scale sterile neutrino dark matter ν s is possible to be detected in β decay experiment using radioactive sources such as 3 T or 106 Ru. The signals of this dark matter candidate are mono-energetic electrons produced in neutrino capture process ν s +N → N +e − . These electrons have energy greater than the maximum energy of the electrons produced in the associated decay process N → N + e − +ν e . Hence, signal electron events are well beyond the end point of the β decay spectrum and are not polluted by the β decay process. Another possible background, which is a potential threat to the detection of ν s dark matter, is the electron event produced by the scattering of solar neutrinos with electrons in target matter. In this article we study in detail this possible background and discuss its implication to the detection of keV scale sterile neutrino dark matter. In particular, bound state features of electrons in Ru atom are considered with care in the scattering process when the kinetic energy of the final electron is the same order of magnitude of the binding energy. Many aspects of this warm DM candidate, e.g. the production mechanism in the early universe [5,[7][8][9][10][11], the astrophysical and cosmological constraints, possible models and symmetries, etc., have been analyzed and considered [12][13][14][15][16][17][18][19][20][21][22] model-independently or in special models. Among them, attention has been paid to the detection of this keV scale DM. It was realized that indirect detection of this DM background in the universe to a good sensitivity can be achieved in principle using satellite observation of monoenergetic X-rays produced in two-body decay of the DM: ν s → ν + γ. However this observation scheme requires large statistics which is not available in present scale satellite observation program [23]. Direct detection of this DM candidate in laboratory has also been investigated [3,4,[24][25][26][27][28]. Because of its small mass and weak interaction, some authors found it not possible to detect this DM candidate in laboratory [25][26][27][28].In a previous work we proposed that keV scale ν s DM can be detected using β decay This type of background should be discussed in detail, which however was not done in detail in [3], for the following reasons: 1) solar neutrinos with higher energy can also participate in the scattering process and the total solar neutrino flux contributing to the background events is significantly higher than that for the first type background; 2) since

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