arXiv:1404.3676v1 [hep-ph] 14 Apr 2014
3.5 keV X-ray Line Signal from Decay of Right-Handed Neutrino
due to Transition Magnetic Moment
Kamakshya Prasad Modak1, ∗
1Astroparticle Physics and Cosmology Division,
Saha Institute of Nuclear Physics, Kolkata 700064, India
We consider the dark matter model with radiative neutrino mass generation where
the Standard Model is extended with three right-handed singlet neutrinos (N1, N2
and N3) and one additional SU(2)L doublet scalar η. One of the right-handed neutri-
nos (N1), being lightest among them, is a leptophilic fermionic dark matter candidate
whose stability is ensured by the imposed Z2 symmetry on this model. The second
lightest right-handed neutrino (N2) is assumed to be nearly degenerated with the
lightest one enhancing the co-annihilation between them. The eﬀective interaction
term among the lightest, second lightest right-handed neutrinos and photon contain-
ing transition magnetic moment is responsible for the decay of heavier right-handed
neutrino to the lightest one and a photon (N2 → N1 + γ). This radiative decay
of heavier right-handed neutrino with charged scalar and leptons in internal lines
could explain the X-ray line signal ∼ 3.5 keV recently claimed by XMM-Newton
X-ray observatory from diﬀerent galaxy clusters and Andromeda galaxy (M31). The
value of the transition magnetic moment is computed and found to be several orders
of magnitude below the current reach of various direct dark matter searches. The
other parameter space in this framework in the light of the observed signal is further
investigated.
∗ kamakshya.modak@saha.ac.in

2
I. INTRODUCTION
One of the enigmas of modern particle physics is dark matter (DM) which, according
to the recent survey of PLANCK [1], consists of ∼ 26.8% of the total energy content of
the universe. Various astrophysical and cosmological observations [2–4] strongly suggest
convincing hints of the existence of dark matter which is non-relativistic or cold in nature.
The particle nature of dark matter is still unknown. The weakly interacting massive particles
(WIMPs) are the most promising candidates for cold dark matter.
The experimental techniques for the detection of dark matter for both direct and indirect
cases are very challenging. In direct detection experiments, the recoil energy of the target
nucleus scattered oﬀ by DM particle is measured whereas the signatures of the annihilations
of decays of DM particles such as charged particles, photons and neutrinos etc. are aimed
to detect in indirect searches. The monochromatic line feature of such decay or annihilation
products of DM are particularly signiﬁcant in predicting the nature of DM particles. A huge
variety of DM models in the framework of WIMP scenario with masses of DM spanning
from keV to TeVs has been addressed in several literatures and their direct and indirect
detection prospects have been widely studied [5–17].
Recently an evidence of X-ray line of energy 3.55 keV with more than 3σ CL has been
reported from the analysis of X-ray data of 73 galaxy clusters from XMM-Newton obser-
vatory [18]. Another group has also claimed a similar line (3.52 keV X-ray line at 4.4σ
CL) from the data of X-ray spectra of Andromeda galaxy (M31) and Perseus cluster [19].
The galaxy clusters are assumed to contain huge amount of DM. Thus the signal may have
a possible origin related to DM. The observed line has been explained as decay of sterile
neutrino dark matter (νs → ν + γ) with mass of the sterile neutrino 7.06 ± 0.05 keV and
mixing angle sin2(2θ) = (2.2 − 20) × 10−11 [19]. Recently many other interesting ideas have
been proposed to explain this line signal to come from DM [20–41].
The neutrino oscillation data [42–45] provide strong evidences for neutrino mass. The
non-zero neutrino masses and evidences of DM give hints to the physics beyond the Standard
Model (SM). The two beyond SM phenomenon, namely the origin of neutrino masses and the
existence of cold dark matter may have a connection. In this work we focus on the simplest
framework which invokes this idea of connecting both sectors has been proposed by Ma [46].
In this model the neutrino masses are generated via radiative processes with only the DM

3
particles in the loop. The right-handed neutrino which can be a possible DM candidate
interacts with lepton doublets and hence DM in this scenario is leptophilic in nature. The
imposed discreet Z2 symmetry on this model not only forbids the tree-level Dirac mass
terms but also assure a stable cold DM candidate. Phenomenological prospects for DM in
this model have been done in Refs. [47–53]. In this paper we consider the case where the
lightest right-handed neutrino (N1) is the cold DM candidate and the second lightest right-
handed neutrino (N2) is nearly degenerated with the cold DM candidate. This situation
provides rich phenomenology in direct detection of such dark matter candidate [54]. Elastic
scattering cross section for DM-nucleon interaction is suppressed in this case and inelastic
scattering that occurs radiatively dominates. The transition from N2 to N1 gives rise to
monochromatic photon with energy equal to the mass diﬀerence between the lightest and
second lightest right-handed neutrinos. If the mass diﬀerence between N2 and N1 is of ∼
keV, then the recent observation of X-ray line can be accommodated in this beyond SM
scenario.
The paper is organised as follows. In Sec. I the theoretical framework of the model is
brieﬂy discussed. Explanation of the observed X-ray line in this model framework and a
study of the constrained parameter space are done in the next section. In Sec. IV a brief
summery of this work and some conclusions are drawn.
II. THE MODEL
We consider the model proposed by Ma [46] which is the extension of Standard Model
with three gauge singlet right-handed neutrinos N1, N2, N3 and and extra SU(2)L doublet
scalar η. The ﬁelds can be written as,
N1, N2, N3, η =

 η+
η0

 . (II.1)
The doublet scalar η is assumed to obtain no vacuum expectation value and hence inert.
An additional discreet Z2 symmetry is imposed on the model. The stability of the cold dark
matter candidate in this model is guaranteed by this symmetry. Not only that the tree-level
Dirac masses of neutrinos are forbidden for this additional Z2 symmetry. SM gauge group
and Z2 charges of the particles are shown in Tab. I.

100%

3.5 keV X-ray Line Signal from Decay of Right-Handed Neutrino due to Transition Magnetic Moment

Scan to connect with one of our mobile apps

Coinbase Wallet app

Coinbase app

Or try the Coinbase Wallet browser extension