Theoretical bounds on dark matter masses

In summary, a recent study found that quantum gravity imposes lower and upper limits on the masses of dark matter candidates, depending on their spins and interactions. For example, the mass range for singlet scalar dark matter is estimated to be between 10^-3 eV and 10^7 eV, with the lower bound coming from limits on fifth force type interactions and the upper bound from the particle's lifetime. This study also rules out the possibility of ultra-light or super-heavy dark matter particles, unless there is an undiscovered force at play. These findings could help narrow down the search for dark matter particles in the future.
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TL;DR Summary
Bounds on mass of dark matter particles.
It looks as if ultra-light and super-heavy have become less likely.

XavierCalmet - FolkertKuipers said:
Abstract
In this letter, we show that quantum gravity leads to lower and upper bounds on the masses of dark matter candidates. These bounds depend on the spins of the dark matter candidates and the nature of interactions in the dark matter sector. For example, for singlet scalar dark matter, we find a mass range ##10^{-3}eV < m_\phi < 10^{7}eV##. The lower bound comes from limits on fifth force type interactions and the upper bound from the lifetime of the dark matter candidate.
https://www.sciencedirect.com/science/article/pii/S0370269321000083
 
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Impressive, although, as noted in another recent thread, this is limited to dark matter candidates that interact solely via gravity with no fifth forces allowing very weak interaction with Standard Model particles or of more than very feeble interactions of these dark matter particles with each other.

But the shape of inferred dark matter halos, and the tight alignment between inferred dark matter distributions and baryonic matter distributions strongly suggest that any dark matter particle model that accurately describes the real work needs one or both of these types of new forces.

The low end of the range is about the mass of the lightest neutrino mass eigenstate. The high end of the range if about 10 MeV, more than an up quark, down quark, electron or any of the three neutrino mass eigenstates, but less than a muon, strange quark, pion (the lightest composite Standard Model particle), and also less than any of the fundamental massive bosons of the Standard Model (the W, the Z and the Higgs boson).

The primary candidate dark matter particles in this mass range are known as "warm dark matter" with a favored mass on the order of 1-10 keV and sterile neutrino dark matter, and aren't necessarily mutually exclusive. This paper would appear to rule out very light axion-like particles with these properties (collisionless and with no non-gravitational interactions) and also particles in the WIMP (weakly interacting massive particle) mass range of about 1-1000 GeV.

Their findings – due to be published in Physical Letters B in March - radically narrow the range of potential masses for Dark Matter particles, and help to focus the search for future Dark Matter-hunters. The University of Sussex researchers used the established fact that gravity acts on Dark Matter just as it acts on the visible universe to work out the lower and upper limits of Dark Matter’s mass. The results show that Dark Matter cannot be either ‘ultra-light’ or ‘super-heavy’, as some have theorised, unless an as-yet undiscovered force also acts upon it. The team used the assumption that the only force acting on Dark Matter is gravity, and calculated that Dark Matter particles must have a mass between 10^-3 eV and 10^7 eV. That’s a much tighter range than the 10-^24 eV - 10^19 GeV spectrum which is generally theorised.
From here. The abstract states that:
In this letter, we show that quantum gravity leads to lower and upper bounds on the masses of dark matter candidates. These bounds depend on the spins of the dark matter candidates and the nature of interactions in the dark matter sector. For example, for singlet scalar dark matter, we find a mass range 10^−3 eV≲mϕ≲10^7 eV. The lower bound comes from limits on fifth force type interactions and the upper bound from the lifetime of the dark matter candidate.
The body text states early on (end notes omitted) that:
In general, quantum gravitational effects will lead to a decay of any dark matter candidate that is not protected by Lorentz invariance or a gauge symmetry from decaying. Furthermore, gravity is universal, it will thus couple to all forms of matter and it will create portals between the Standard Model and any hidden sector. While these decays will be suppressed by powers of the Planck mass, they will still lead to an upper bound on dark matter particles given the large age of our universe. Furthermore, if the dark matter particles are light, the same quantum gravitational effects will lead to fifth force type interactions and these interactions are bounded by limits coming from the Eöt-Wash experiment. Finally, there is a well known lower bound coming from quantum mechanics and more specifically the spin-statistics theorem which applies to fermionic dark matter candidate. This last bound depends on the dark matter profile.

Putting all these bounds together, we obtain tight mass ranges for scalar, pseudo-scalar, spin 1/2 and spin 2 dark matter particles which are gauge singlets. These bounds can be relaxed if the fields describing these particles are gauged, we however note that there are fairly tight constraints on the strength of the interactions in the dark matter sector. Finally, we argue that spin-1 vector dark matter particles are less constrained by quantum gravity, because of the chiral nature of the fermions in the Standard Model.
 
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