There is no Majorana Fermion Dark Matter

Anapole Dark Matter at the LHC

Yu Gao, Chiu Man Ho, Robert J. Scherrer
(Submitted on 22 Nov 2013)

The anapole moment is the only allowed electromagnetic moment for Majorana fermions. Fermionic dark matter acquiring an anapole can have a standard thermal history and be consistent with current direct detection experiments. In this paper, we calculate the collider monojet signatures of anapole dark matter and show that the current LHC results exclude anapole dark matter with mass less than 100 GeV, for an anapole coupling that leads to the correct thermal relic abundance.

From the paper (citations omitted):

The nature of the dark matter that constitutes most of the nonrelativistic density in the universe remains unresolved. While the leading candidates are usually considered to be either a massive particle interacting via the weak force (WIMP), or an axion, there has been a great deal of recent interest in the possibility that the dark matter interacts electromagnetically. Dark matter with an integer electric charge number ∼ O(1) has long been ruled out, and even millicharged dark matter is strongly disfavored. Hence, the most attention has been paid to models in which the dark matter particle has an electric or magnetic dipole moment, which we will call generically dipole dark matter (DDM). If one assumes a thermal production history for the dark matter, fixing the dipole moment coupling to provide the correct relic abundance, then the corresponding rate in direct detection experiments rules out a wide range of DDM mass.

An alternative to DDM is a particle with an anapole moment. The idea of the anapole moment was first proposed by Zel’dovich and mentioned in the context of dark matter by Pospelov and ter Veldhuis. More recently, the properties of anapole dark matter (ADM)
were investigated in detail by Ho and Scherrer. (See also the model of Fitzpatrick and Zurek, in which the anapole couples to a dark photon rather than a standard-model photon). Anapole dark matter has several advantages over DDM. The anapole moment is the only allowed electromagnetic moment if the dark matter is Majorana, rather than Dirac. The annihilation is exclusively p-wave, and the anapole moment required to give the correct relic abundance produces a scattering rate in direct detection experiments that lies below the currently excluded region for all dark matter masses (although see our discussion of LUX in Sec. V). . . .

In [a recent study], it was shown that the differential scattering rate for anapole dark matter at direct detection experiments reaches a maximum around mχ ∼ 30 − 40 GeV and it lies just below the threshold for detection by XENON100. Given the significantly improved sensitivity around this regime by LUX, it may be possible that anapole dark matter with mχ ∼ 30 − 40 GeV is ruled out. However, we have just shown that the current LHC results have already excluded anapole dark matter with mχ < 100 GeV. So the new bounds from LUX are redundant for mχ < 100 GeV. For mχ > 100 GeV, the annihilation channels χχ → W+W− and χχ → tt¯ open up and the correct relic abundance is achieved with a much smaller gA. Since the differential scattering rate is proportional to gA, the analysis in [that recent study] indicates that the bound from LUX on anapole dark matter with mχ > 100 GeV is far too loose to exclude this mass range.

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A Majorana fermion is a particle with non-integer spin that is its own antiparticle.

Neither quarks nor charged leptons fit this description, and it is not yet determined whether Standard Model neutrinos fit this description or instead have "Dirac mass."  The combined non-detection of neutrinoless double beta decay in all neutrinoless double beta decay experiments to date that are credible in the scientific community current limit the Majorana mass of neutrinos to no more than 100-150 meV, with the greatest likelihood estimates of the sum of the masses of all three types of neutrinos in a "normal hierarchy" currently at about 60 meV.  If neutrinoless double beta decay experiments reduce this bound by a factor of two to three, at least some neutrino mass will have to be non-Majorana, and an order of magnitude improvement in the bound, which is realistic in the next decade or so, should be capable of entirely resolving the nature of neutrino mass.

This paper basically rules out the possibility of light Majorana Fermion dark matter.

We further know that, for reasons generally applicable in cold dark matter v. warm dark matter comparisons, dark matter with masses of 100 GeV or more are a poor fit to the experimental evidence.

So, Majorana Fermion dark matter is basically ruled out by the totality of the evidence.

Cultural footnote:  Contemporary fantasy writer L.J. Smith (best known for her "Vampire Diaries" teen fiction series that has been adapted in to a many season television show), deserves credit for creating a female high school student character in her 1996 novel, "Daughters of Darkness" in her "Night World" series, who is thinking seriously about a career in astronomy and has research interest, including research into the distribution of dark matter in the universe or supernova properties with tools including orbital telescopes, that are closely in line with what real astronomers are still studying in 2013 (around the time that the character in the book would probably have recently become an associate professor and possibly leading some of these research projects).