A 7 keV sterile neutrino is a good candidate for warm dark matter.
What are the feynman diagrams by which a 7 keV sterile neutrino can be produced?
What are the decay channels? By which diagram can it decay to 2 photons so that a sharp line at 3.5 keV can be seen?
I am no expert, but I think that the minimal phenomenology starts with a massive family of neutrino N_I in the Lagrangian, that mix to the active neutrinos of the SM. The sterile neutrino DM candidate is a mass eigenstate, so it is a mixing of the sterile and active neutrinos, and thus is created (~ at QCD scale) or decay through mixing to the active neutrinos. Then you can add scalar fields that couple to the N_I. Etc...
The 3.5 keV line comes from a subdominant N_I->nu gamma channel
Johan, Let us confine ourselves to dim-4 mass terms in the
Lagrangian. Then a nu N_1 term should be there with a scalar.
Counting mass dimensions 3/2+3/2+1=4. Because nu is a
doublet with hypercharge -1/2, the Higgs should be a doublet
with hypercharge +1/2. This is like the usual doublet Higgs VEV
that is causing the mixing. That means N_1 is decaying to
a Higgs and a normal neutrino. This diagram is used in
Leptogenesis also. But the decay rate will be too fast unless
the Yukawa coupling is fine tuned to be too small. I think
this is because the lifetime of N_1 must be comparable to the
lifetime of the universe.
The most economical way (and for some the most natural way) to treat neutrino masses is to have both a Majorana and a Dirac mass term. The Dirac mass corresponds to a left handed (active) to right handed neutrino (sterile) transition and the Majorana mass term corresponds to a left-handed neutrino (active) to a right handed anti-neutrino (also active). What thus requires sterile neutrinos is the existence of a Dirac mass term like all other fermions of the Standard Model. The Majorana mass term violates fermion number conservation, but there is no such quantum number conservation in the Standard Model, it is only an *apparent* conservation due to the combination of charge conservation (for charged fermions) and angular momentum conservation (for massless neutrinos).
Now one has four states for each neutrino species or 12 for all neutrinos families. They mix in all possible ways due to the transitions that exist between left and right handedness, between flavours and between 'charge' (both being defined as the flavour and charge of the lepton produced in a weak interaction of the neutrino). The particle that propagate in vacuum are eigenstates of mass, spin and electric charge not of the above, so there appear "almost sterile" neutrinos which have a small active component.
The mixing is typically of the order of mD/mM (Dirac mass divided by Majorana mass) and in absence of knowledge of mD and mM it can be very small. The lightest mass state is are the 'mostly active' neutrinos (those we know) and the heavier ones are 'almost sterile'. The usual wisdom would be that mD is similar to the top quark mass, and that mM should be almost of the order of the GUT scale (10^10 GeV?) but really we dont know, especially if there are three families. This is then an open question: why should mD not be of the same size as the electron mass, or even much smaller since neutrinos have no charge? The lightest neutrino state has a mass of order mD^2/mM i.e. Theta.mD. In arXiv:1208.4607, Shaposhnikov and collaborators find that the lightest of the 'almost sterile' neutrinos could have a mass of 10 keV and have a coupling sufficient to be produced in the early universe; and now in equilibrium within stars, as fraction of the normal neutrino-producing reactions; and be sterile enough to decay very slowly. In this scenario the heavier 'almost sterile' neutrinos can have masses of the order of the electroweak scale (GeV to 100 GeV) and be possibly searched for in heavy flavour decays, or at a Z factory such as TLEP (see DOI 10.1007/JHEP01(2014)164 or arXiv:1308.6176v3 [hep-ex] ) . The article arXiv:1208.4607, explain also that the heavy 'almost sterile' neutrinos can be involved in generating the baryon asymmetry of the Universe.
This scheme (the vSM) is gaining popularity as the most economical scenario to explain both the dark matter and the baryon asymmetry of the universe. But of course it remains to explain what generates the Majorana mass term!
Dear Prof. Blondel,
I cannot follow your comment exactly. I think you are considering
Dirac neutrinos. Then there are three right handed neutrinos.
So total six neutrino states. These states will have a six by six
mass matrix. After diagonalization three will be heavy and three
will be light. The light ones are active whereas the heavy ones
are almost sterile. Is this what you mean ?
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